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Appendix:Glossary of basketball

Basketball, like any other major sport, has its own unique words and phrases used by sports journalists, players, and fans.

0–9

 * 24-second violation: Inability of a team to shoot before the shot clock expires.
 * 3-and-D: a player, usually not a star, who specializes in three-point shooting ("3") and defense ("D"). Most commonly associated with the NBA, where this type of player has been increasingly valued in the 21st century.
 * 50–40–90 club: a notional club consisting of players who have shooting percentages of 50% on field goals, 40% on three-pointers, and 90% on free throws in a given season. Can be applied to any league, but most commonly associated with the NBA.

A

 * air ball: An unblocked shot that fails to hit the rim or backboard. If the shooting team grabs the rebound, the shot clock (if there is one) will not be reset.

 * assist: Passing the ball to a teammate who immediately scores a basket after receiving a pass. The teammate that receives the pass may take one dribble before shooting.

B

 * ball hog : A player who attempts to monopolize his play of the ball, usually shooting excessively.
 * buzzer beater : The final shot of a game that in itself results in a win or overtime.

C

 * center: One of the three standard player positions, centers are usually the tallest player on the team and are responsible for defending the basket and rebounding.
 * crescent cut: a cut where the offensive player runs in an arc instead of sharply changing direction. Usually this cut starts opposite the player with the ball and moves toward the ball and then to the basket.

D

 * downtown: The area on the offensive side of the three-point line.

F

 * FIBA: The International Basketball Federation, an association of national organizations which governs international competitition.
 * forward : One of the three standard player positions, forwards are primarily responsible for scoring and rebounding. See small forward and power forward.
 * free throw : An unopposed attempt to score a basket, worth one point, from the free throw line. Generally, two attempts are awarded when the player is fouled in the act of shooting, fouled flagrantry, or when the opposing team fouls while over the foul limit. One attempt is awarded for technical fouls.
 * FUBAR : Fine Upper Ball Arm Reach, the ability to scoop the ball up from high under intense pressure.

G

 * guard : One of the three standard player positions, guards usually are responsible for setting up offensive plays. See point guard and shooting guard.

I

 * in-n-out : a shot that appears to be sailing in, but doesn't drop.

L

 * lay up: a field goal attempt made by below,laying the ball up near the basket,and using one hand to tip the ball over the rim and into the basket(layin)or to bank it off the backboard and into the basket(layup)

M
Motion Offense---Offense created through a series of cuts and screens to create the best possible shot, with most or all offensive players moving simultaneously.

N

 * NBA : The National Basketball Association, the largest professional league in the United States.

O

 * offensive foul

P

 * penetration : When an offensive player, dribbling and handling the ball, gets into the key or past defenders.
 * pick :See setting a screen
 * point : A point is scored by successfully passing the ball through the basket. A free throw is worth one point, a field goal is worth two points, and a three-point shot is worth three points.
 * point guard : A position normally played by the smallest player on the team, who is responsible for controlling the offense and distributing the ball to the right players at the right time.

R
RIP A C

A motion used while chinning the ball to create space during a pivot between you and the defender. Pivot towards the defender and rip the ball in a C shape away from the pressure to create a passing lane.

S

 * setting a screen :A legal attempt by an offensive player to stop an opponent from guarding a teammate, by standing in the defender's way such that the teammate cuts next to him, blocking the defender. The teammate is now open to receive a pass, make a shot or cut to the basket. The player setting the pick must remain stationary; a moving screen is illegal and may result in an offensive foul. Also called a "pick".

 * stretch four : A power forward ("four") who can shoot three-pointers well enough to force a defense to guard him or her behind the arc, thereby "stretching" the defense.

T

 * technical foul : A foul most commonly associated with unsportsmanlike behavior. However, some procedural violations are also technical fouls.  The term is frequently abbreviated to simply "tech."

 * three-point field goal : A shot attempted anywhere from behind the three-point line of the defending team that, if successful, is worth three points.

 * three-point play : A situation where a player is fouled but completes the basket, sending them to the free throw line with the opportunity to convert a two-point play into three. The phrase "and one" is also commonly used by commentators.

U

 * ULEB : A European body of men's basketball leagues that organized the continent's two largest club competitions, the Euroleague and Eurocup, before handing responsibility to the Euroleague Basketball Company.

W

 * WNBA : The Women's National Basketball Association, the largest professional basketball league for women in the United States.

 * wolf : Term that is shouted to alert the ball handler that someone is coming from behind.

title: Appendix:Glossary of basketball


text:
exprobrate

Verb

 * 1)  To reproach or upbraid

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: exprobrate


text:
reflexed

Adjective

 * 1) turned backwards

title: reflexed


text:
cave canem

Etymology
Literally “Beware of the dog”.

Phrase

 * 1) beware of the dog

title: cave canem


text:
Appendix:Glossary of climbing and mountaineering

This page is a glossary of the jargon related to climbing and mountaineering.

A

 * ablation zone : The area of a glacier where yearly melting meets or exceeds the annual snow fall.
 * abseil : The process by which a climber may descend a fixed rope. Also known as rappel.
 * adze : A thin blade mounted perpendicular to the handle on an ice axe that can be used for chopping footholds.
 * alpine start : To make an efficient start on a long climb by packing all your gear the previous evening and starting early in the morning, usually well before sunrise.
 * altitude sickness : A medical condition that is often observed at high altitudes. Also known as Acute mountain sickness, or AMS.
 * anchor :An arrangement of one or (usually) more pieces of gear set up to support the weight of a belay or toprope
 * approach : The path or route to the start of a technical climb. Although this is generally a walk or, at most, a scramble it is occasionally as hazardous as the climb itself.
 * arête : An outside corner of rock. Also a method of indoor climbing, in which one is able to use such a corner as a hold. See also dihedral.
 * ascender : A device for ascending on a rope. One type of mechanical ascender is the  jumar.
 * ATC : A proprietary type of belay device. (A subtle play on fact that ATC also stands for Air traffic controller.)

B

 * "B"-grade : A grading system for bouldering problems, invented by . Now largely superseded by the "V" grading system.
 * back-clipping : A hazardous mistake that can be made while lead climbing. The belay rope is clipped into a quickdraw in the wrong direction causing an increase in friction on the rope and an increase in the likelihood of the rope becoming unclipped during a fall.
 * bail : To retreat from a climb.
 * barn-dooring : Swinging out from the wall like a door on a hinge.
 * belay : To protect a climber from falling using a rope, friction, and an anchor.
 * belay device : A mechanical device used to create friction when belaying by putting bends in the rope. Many types of belay device exist, including ATC, grigri, Reverso, Sticht plate, eight, and tuber. Some belay devices may also be used as descenders. A Munter hitch can sometimes be used instead of a belay device.
 * belay slave : Someone that volunteers for, or is tricked into, repeated belaying duties without partaking in any of the actual climbing.
 * Bergschrund (or schrund): A crevasse that forms on the upper portion of a glacier where the moving section pulls away from the headwall. Also called a 'shrund.
 * beta : Advice and/or instructions on how to successfully complete a particular climbing route.
 * beta flash : Ascent of a climb on the first attempt with some knowledge beta of that climb, with no falls or hangdogging. Also see on-sight.
 * biner : See carabiner.
 * bivy (or bivvy): A camp, or the act of camping, from "bivouac." On a big wall, camp can be made on a natural ledge or an artificial one, generally a cotlike device called a portaledge that hangs from anchors on the wall.
 * bivy-bag : A lightweight garment or sack offering full-body protection from wind and rain.
 * bollard : A large knob of rock or ice used as a belay anchor.
 * bolt : A point of protection permanently installed in a hole drilled into the rock, to which a metal hanger is attached, having a hole for a biner or ring.
 * bolt chopping : The deliberate and destructive(and sometimes justified) removal of one or more bolts.
 * bomb-proof anchor : A totally secure anchor. Also known as a bomber. Anchors are often misclassified as such.
 * bouldering : The practise of climbing on large boulders. Typically this is close to the ground, so protection takes the form of crash pads and spotting instead of belay ropes.
 * bump : To quickly move up a hand or a foot a small distance from one useful hold to another.
 * bucket : A large handhold.
 * buildering : The art of climbing on buildings, which is often illegal.
 * buttress : A prominent feature that juts out from a rock or mountain.

C

 * cairn : A distinctive pile of stones placed to designate a summit or mark a trail above treeline.
 * cams : A spring-loaded device used as protection. See spring loaded camming device.
 * campus board : Training equipment used to build finger strength and strong arm lock-offs.
 * carabiner : Metal rings with spring-loaded gates, used as connectors. Also known as crab or biner.
 * chalk : A compound used to improve grip by absorbing sweat. It is actually gymnastics chalk, usually magnesium carbonate. Its use is controversial in some areas.
 * chalk bag : A hand-sized holder for a climber's chalk that is usually carried on a chalkbelt for easy access during a climb.
 * chimney : A rock cleft with vertical sides mostly parallel, large enough to fit the climber's body into. To climb such a structure, the climber often uses his head, back and feet to apply opposite pressure on the vertical walls.
 * The process of using such a technique.

 * chock : A mechanical device, or a wedge, used as anchors in cracks.
 * A naturally occurring stone wedged in a crack.

 * choss : Loose or "rotten" rock.
 * classification : See Grade.
 * clawing : Use of front points of crampons, ice axe pick and ice hammer pick to climb a slope.
 * clean : To remove equipment from a route.
 * A route that is free of loose vegetation and rocks.
 * To complete a climb without falling or resting on the rope. Also see redpoint.
 * In aid climbing, abbreviated "C", a route that does not require the use of a hammer or any invasive addition of protection (such as pitons or copperheads) into the rock (see protection).

 * cleaning tool : A device for removing jammed equipment, especially nuts, from a route. Also known as a nut key.
 * climbing area : A region that is plentiful with climbing routes.
 * climbing command : A short phrase used for communication between a climber and a belayer.
 * climbing gym : Specialized indoor climbing centres. See gym climbing.
 * climbing shoe : Footwear designed specifically for climbing. Usually well fitting, with a rubber sole.
 * climbing wall : Artificial rock, typically in a climbing gym.
 * clipping in : The process of attaching to belay lines or anchors for protection.
 * Col : A small pass or "saddle" between two peaks. Excellent for navigation as when standing on one it's always down in two, opposite, directions and up in the two directions in between those.
 * couloir : A steep gully or gorge frequently filled with snow or ice.
 * cornice : An overhanging edge of snow on a ridge.
 * Crack climbing : To ascend on a rock face by wedging body parts into cracks, i.e. not face climbing. See jamming and chimney.
 * crag : A small area with climbing routes, often just a small cliff face or a few boulders.
 * crampons : Metal framework with spikes attached to boots to increase safety on snow and ice.
 * cramponing : Using crampons to ascend or descend on ice, preferably with maximum number of points of the crampon into the ice for weight distribution.
 * Accidentally piercing something with a crampon spike.

 * crank : To pull on a hold as hard as possible.
 * crash pad : A thick mat used to soften landings or to cover hazardous objects in the event of a fall. See: bouldering mat
 * crater : Hitting the ground at the end of a fall instead of being caught by the rope.
 * crimp : A small but positive hold, with very little surface area. See also Nub.
 * The process of holding onto a crimp.

 * crux : The most difficult portion of a climb.
 * cut-loose : Where a climber's feet swing away from the rock on overhanging terrain, leaving the climber hanging only by their hands.

D

 * daisy chain : A special purpose type of sling with multiple sewn, or tied, loops. It is significantly weaker than a normal sling.
 * dead hang : To hang limp, such that weight is held by ligament tension rather than muscles.
 * deadman anchor : An object buried into snow to serve as an anchor for an attached rope. One common type of such an anchor is the snow fluke.
 * deadpoint :A dynamic climbing technique in which the hold is grabbed at the apex of upward motion. This technique places minimal strain on both the hold and the arms.
 * Deck : The ground.
 * To hit the ground, usually the outcome of a fall.

 * descender : A device for controlled descent on a rope. Many belay devices may be used as descenders, including ATCs, eights, or even carabiners.
 * dialled : To have complete understanding of a particular climbing move or route.
 * Diamox : A drug used to inhibit the onset of altitude sickness. Otherwise known as Acetazolamide.
 * Dièdre : A dihedral.
 * dihedral : An inside corner of rock, with more than a 90-degree angle between the faces. See also arête.
 * direct aid : A type of tension climbing consisting of using one or more belay ropes to haul the leader up to the next point of protection.
 * downclimb : To descend by climbing downward, typically after completing a climb.
 * dry tooling : Using tools for ice climbing like crampons and ice axes on rock.
 * Dulfersitz : A method of rappelling, without mechanical tools, where the uphill rope is straddled by the climber then looped around a hip, across the chest, over the opposite (weak) shoulder, and held with the downhill (strong) hand to adjust the shoulder friction and thus the descending speed.
 * dynamic belay : Technique of stopping a long fall using smooth braking to reduce stress on the protection points and avoid unnecessary trauma from an abrupt stop.
 * dynamic rope : A slightly elastic rope that softens falls to some extent. Also tend to be damaged less severely by heavy loads. Compare with static rope.
 * dynamic motion : Any move in which body momentum is used to progress. As opposed to static technique where three-point suspension and slow, controlled movement is the rule.
 * dyno : A dynamic move to grab a hold that would otherwise be out of reach. Generally both feet will leave the rock face and return again once the target hold is caught. Non-climbers would call it a jump or a leap.

E

 * edge : A thin ledge on the rock.
 * edging : Using the edge of the climbing shoe on a foothold.
 * Egyptian : A climbing technique used to reduce tension in arms while holding a side grip.
 * eight-thousander : A mountain that tops 8,000 metres.
 * eliminate : A term from bouldering describing a move or series of moves in which either certain holds are placed 'off bounds' or other artificial restrictions are imposed.
 * exposure : Empty space below a climber, usually referring to a great distance above the deck through which the climber could fall.

F
A usually insecure fin or flake of rock or ice.
 * face climbing : To ascend a vertical rock face using finger holds, edges and smears, i.e. not crack climbing.
 * fall : Undesirable downward motion. Hopefully stopped by a rope, otherwise see mountain rescue.
 * figure four : Advanced climbing technique where the climber hooks a leg over the opposite arm, and then pushes down with this leg to achieve a greater vertical reach. Requires strength and a solid handhold.
 * finger board : Training equipment used to build finger strength.
 * first ascent : The first successful completion of a route.
 * fist jam : A type of jam using the hand.
 * fixed rope : A rope which has a fixed attachment point. Commonly used for abseiling or aid climbing.
 * flagging : Climbing technique where a leg is held in a position to maintain balance, rather than to support weight. Often useful to prevent barn-dooring.
 * flake : A thin slab of rock detached from the main face.
 * flapper : An injury consisting of a piece of loose (flapping) skin. A climber will usually just repair these with sticky tape or super glue.
 * Flash : To successfully and cleanly complete a climbing route on the first attempt.
 * follow : What the second does.
 * fourteener : Mountain that tops 14,000 feet in the contiguous United States.
 * free climbing : Climbing without unnatural aids, other than used for protection.
 * friction : Climbing technique relying on the friction between the sloped rock and the sole of the shoe to support the climber's weight, as opposed using holds or edges, cracks, etc.
 * friend : A name brand of a type of spring loaded camming device (SLCD), sometimes used to refer to any type of spring loaded camming device.
 * flute:

G

 * gaston : A type of climbing grip. Best described as a handhold that is only good from the side, but you must hold it with your elbows pointing out.
 * gendarme : A pinnacle or isolated rock tower frequently encountered along a ridge.
 * Geneva rappel : A modified dulfersitz rappel using the hip and downhill arm for friction, rather than the chest and shoulder, offering less complexity, but less friction and less control.
 * glacier travel : walking or climbing on a glacier; a rope is usually used to arrest falls into crevasses, but protection is not used.
 * glissade : A usually voluntary act of sliding down a steep slope of snow.
 * gorp : Trail mix for periodic nibbling to keep high energy level between meals on long climbs or hikes. An acronym for 'Good Ol' Raisins & Peanuts'
 * Grade : Intended as an objective measure of the technical difficultly of a particular grade climb or bouldering problem. More often is highly subjective, however.
 * A surveying term for referring to the slope of an incline.

 * grigri : A belay device designed to be easy to use and safer for beginners because it is self-locking under load. Invented and manufactured by Petzl. Many experienced climbers advocate the use of an atc type device for beginners
 * gripped : Scared. Also over gripping the rock.
 * grovel : To climb with obviously poor style or technique.
 * A climbing route judged to be without redeeming virtue.

 * gumby : An inexperienced (or unsafe) climber.
 * Gym climbing : Climbing indoors, on artificial climbing walls. This is typically for training but many people consider this a worthwhile activity in its own right.

H

 * HACE (acronym): high altitude cerebral edema - a severe, and often fatal, form of altitude sickness.
 * hand traverse : Traversing without any definitive footholds, i.e. smearing or heelhooking.
 * hangdog : While lead climbing or on top rope, to hang on the rope or a piece of protection for a rest.
 * hanging belay : Belaying at a point such that the belayer is suspended.
 * HAPE (acronym): High Altitude pulmonary edema - a serious form of altitude sickness.
 * harness : See climbing harness. A sewn nylon webbing device worn around the waist and thighs that is designed to allow a person to safely hang suspended in the air.
 * haul bag : A large and often unwieldy bag into which supplies and climbing equipment may be thrown.
 * headwall : The region of a cliff or rock face that steepens dramatically.
 * helmet : Also known as a brain bucket or skid lid. It can save your life, but only while worn.
 * hexcentric : A protective device. It is an eccentric hexagonal nut attached to a wire loop. The nut is inserted into a crack and it holds through counter-pressure. Often just termed hex.
 * hold : A place to temporarily cling, grip, jam, press, or stand in the process of climbing.
 * honed : To be in peak mental and physical fitness for climbing.
 * hook : Climbing equipment used in aid climbing.
 * A climbing technique.

I

 * ice axe : A handy tool for safety and balance, having a pick/adze head and a spike at the opposite end of a shaft.
 * ice hammer : A lightweight ice axe with a hammer/pick head on a short handle and no spike.
 * ice screw : A screw used to protect a climb over steep ice or for setting up a crevasse rescue system. The strongest and most reliable is the modern tubular ice screw which ranges in length from 18 to 23 cm.
 * ice piton : Long, wide, serrated piton once used for weak protection on ice.
 * indoor climbing : See gym climbing.

J

 * jamming : Wedging a body part into a crack.
 * jug hold : A large, easily held hold. Also known simply as a jug.
 * jumar :
 * 1) A type of mechanical ascender.
 * 2) To ascend a rope using a mechanical ascender.

K

 * Klemheist knot : An alternative to the Prusik knot, useful when the climber is short of cord but has plenty of webbing.
 * knots : Climbers rely on many different knots for anchoring oneself to a mountain, joining two ropes together, slings for climbing up the rope, etc.

L

 * lead climbing : A form of climbing in which the climber places anchors and attaches the belay rope as they climb.
 * leader fall : A fall while lead climbing. A fall from above the climbers last piece of protection.  The falling leader will fall at least twice the distance back to her last piece, plus slack and rope stretch.
 * lieback : Or layback. A climbing move that involves pulling on the hands while pushing on the feet.
 * locking carabiner : A carabiner with a locking gate, to prevent accidental release of the rope.

M

 * mantle : A climbing move used to surmount a ledge or feature in the rock in the absence of any useful holds directly above. It involves pushing down on a ledge or feature instead of pulling down. In ice climbing, a mantle is done by moving the hands from the shaft to the top of the ice tool and pushing down on the head of the tool.
 * The external covering of a climbing rope. Climbing ropes use kernmantle construction consisting of a kern (or core) for strength and an external sheath called the mantle.

 * match : To use one hold for two limbs, or to swap limbs on a particular hold.
 * moat : A crevasse that forms where the glacier pulls away from a rock formation.
 * Mountain rescue : A team of people that may come and rescue you after an injury or accident. May also search for overdue climbers, at no small peril and expense.
 * move : Application of a specific climbing technique to progress on a climb.
 * multi-pitch climbing : Climbing on routes that are too long for a single belay rope.
 * Munter hitch : A simple hitch that is often used for belaying without a mechanical belay device. Otherwise known as an Italian hitch or a Friction hitch.

N

 * névê : Permanent granular ice formed by repeated freeze-thaw cycles.
 * no-hand rest : An entirely leg-supported resting position during climbing that does not require hands on the rock.
 * nub : A little hold that only a few fingers can grip, or the tips of the toes.
 * nunatak : A mountain or rock that protrudes through an ice field.
 * nut : A metal wedge attached to a wire loop that is inserted into cracks for protection. See hexcentric.
 * nut key : See cleaning tool

O

 * objective danger : Danger in a climbing situation which comes from hazards inherent in the location of the climb, not depending on the climber's skill level. Most often these involve falling rock or ice, or avalanches.
 * off-width : A crack that is too wide for effective hand or foot jams, but is not as large as a chimney.
 * on-sight climbing : A clean ascent, with no prior practice or beta.
 * open book : An inside angle in the rock. See also dihedral.
 * overhang : A section of rock or ice that is angled beyond vertical. See roof.

P

 * peak bagging : To systematically attain designated summits under prescribed conditions.
 * peel : To fall.
 * pendulum : Swinging on taut rope to reach the next hold in a pendulum traverse.
 * pickets : Long, tubular rods driven into snow to provide a quick anchor.
 * pinkpoint : To complete a lead climb without falling or resting on the rope (hangdogging), but with pre-placed protection and carabiners. Also see clean and redpoint.
 * pinch hold : This is a hold where you must pinch it to hold on. They come in various sizes.
 * pitch : In the strictest climbing definition, a pitch is considered one rope length (50-60 meters). However, in guide books and route descriptions, a pitch is the portion of a climb between two belay points.
 * piton : A flat or angled metal blade of steel which incorporates a clipping hole for a carabiner or a ring in its body. A piton is typically used in "aid-climbing" and an appropriate size and shape is hammered into a thin crack in the rock and preferably removed by the last team member.
 * pton catcher : clip-on string fastened to piton when inserting or removing, so as to avoid loss.
 * plunge step : An aggressive step pattern for descending on hard or steep angle snow.
 * positive : Of a hold or part of a hold, having a surface facing upwards, or away from the direction it is pulled, facilitating use.
 * pressure breathing : Forcefully exhaling to facilitate O2/CO2 exchange at altitude. Also called the "Whittaker wheeze".
 * protection : Process of setting equipment or anchors for safety.
 * equipment or anchors used for arresting falls. Commonly known as Pro.

 * Prusik : A knot used for ascending a rope. It is named after Dr Karl Prusik, the Austrian mountaineer who developed this knot in 1931.
 * To use a Prusik knot for ascending a rope.

 * pumped : To have such an accumulation of lactic acid in the flexor digitalis (forearm), that forming even a basic grip becomes impossible. Often easy activities such as holding a joint become difficult or impossible.

Q

 * quickdraw : Used to attach a freely running rope to anchors or chocks. Sometimes called "quickies" or just "draws."

R

 * rack : The set of equipment carried up a climb; also, the part of a harness (consisting of several plastic loops) where equipment is hung, ready to be used.
 * rappel : The process by which a climber may descend on a fixed rope using a friction device. Also known as Abseil or roping down..
 * rebolting : The replacement of bolts on an existing climb.
 * redpoint : To complete a lead climb without falling or resting on the rope (hangdogging). Also see clean and pinkpoint.
 * rest step : Energy-saving technique where unweighted (uphill) leg is rested between each forward step, sometimes by "locking" knee of rear leg.
 * retro-bolting : The addition of bolts to an existing climb.
 * roof : Horizontal overhang.
 * rope : An basic item of climbing equipment.
 * route : The path of a particular climb, or a predefined set of moves.
 * runner : Another term for sling.
 * runout : An inordinate span between two points of protection.
 * A long portion of a route with minimal protection.

 * RURP (acronym): stands for Realized Ultimate Reality Piton. Miniature, postage-stamp sized piton originally designed by Yvon Chouinard.

S

 * saddle : A high pass between two peaks, larger than a col.
 * sandbag : A climb which receives a much lower grade than deserved. A traditionally protected climb can, if undergraded, be very dangerous, and the term sandbag is often said with a note of respectful dread.
 * scrambling : Non-technical climbing.
 * screamer :
 * 1) A long and loud fall.
 * 2) A nylon webbing structure consisting of one large loop sewn up in multiple places to make a shorter length.  In the event of a fall the sewn sections part, absorbing some of the fall energy and decelerating the climber.
 * scree : Small, loose, broken rocks, often at the base of a cliff.
 * second : A climber who follows the lead, or first, climber.
 * self-arrest : The act of planting the pick of your ice axe into the snow to arrest a fall in the event of a slip. Also a method of stopping in a controlled glissade.
 * send: Cleanly completing a route. ie on-sight, flash, redpoint. Sometimes even on tr.
 * serac : A large ice tower.
 * sewing machine leg : The involuntary vibration of one or both legs resulting from fatigue or panic. Also known as "Elvis Presley Syndrome", or "Disco knee".
 * sharp end : The end of the belay rope that is attached to the lead climber.
 * side grip : A (usually vertical) hold that needs to be gripped with a sideways pull. Often just simply called a "side pull."
 * sirdar : Head sherpa mountain guide.
 * sit start : Starting a climb from a position in which the climber is sitting on the floor. This is common in climbing gyms in order to fit an extra move into the climb.
 * slab : A relatively low-angle (singinficantly less than vertical) section of rock, usually with few large features. Requires slab climbing techniques.
 * slab climbing : A particular type of rock climbing, and its associated techniques, involved in climbing rock that is less than vertical. The emphasis is on balance, footwork, and making use of very small features or rough spots on the rock for friction.
 * slack : Portion of rope that is not taught, preferably minimized during belay.
 * SLCD : (acronym) Abbreviation for spring loaded camming device, a type of protection device. These are better known by the term cam.
 * sling : Webbing sewn, or tied, into a loop.
 * sloper : A sloping hold with very little positive surface. A sloper is comparable to palming a basketball.
 * smearing : To use friction on the sole of the climbing shoe, in the absence of any useful footholds.
 * snarg : A type of tubular ice screw that is inserted by hammering.
 * snow fluke : An angled aluminium plate attached to a metal cable. The fluke is buried into snow, typically used as a deadman anchor.
 * solo climbing : Climbing without any protection (free solo) or setting and cleaning ones own protection on an ascent.
 * sport climbing : A form of climbing where grace and technical (or gymnastic) ability are considered more important than danger, exhilaration or brute strength. Sport climbing routes tend to be well protected with pre-placed bolt-anchors.
 * spotting : An alternative to belaying commonly used during bouldering. A friend of the climber stands beneath them and prevents awkward falls or falls onto hazards.
 * static : Of a style of climbing or specific move, not dynamic.
 * static rope : A non-elastic rope. Compare with dynamic rope.
 * stem :
 * 1) The simultaneous use of two widely spaced footholds.
 * 2) Climbing using two faces that are at an angle (<180) to each other.
 * sticht plate : A belay device consisting of a flat plate with a pair of slots. Named after the inventor Franz Sticht.
 * stick clip : A device used in sport climbing to clip the first bolt. This is especially useful if the first bolt is high up, and out of the comfort zone of the climber. A stick clip can be bought, or easily made.
 * stopper :
 * 1) A wedge-shaped nut.
 * 2) A knot used to prevent the rope running through a piece of equipment.
 * summit :
 * 1) The summit (or high point) of a mountain or peak.
 * 2) To reach such a high point.
 * swami belt : A kind of proto- climbing harness consisting or a long length of tubular webbing wrapped several times around the climbers body and secured with a water knot. Largely eschewed today in favor of commercial harnesses.
 * swinging-lieback : A dynamic form of the lieback described above, rotating off one foot while maintaining a grip with that hand, then grabbing a high handhold at the deadpoint of the swing. This move if frequently reversible, unlike more aerial dynos.

T

 * talus : Large rock fragments forming an often unstable slope below scree.
 * teabagging : When, after a whipper, or long fall, a climber falls past their belayer, who is generally lifted up off the ground.
 * technical climbing : Climbing involving a rope and some means of protection, as opposed to scrambling or glacier travel.
 * tension : A technique for maintaining balance using a taught rope through a point of protection.
 * thrutching : Bad technique or 'body climbing' specifically at Mount Arapiles.
 * top rope : To belay from a fixed anchor point above the climb.
 * top-out: To go on to the top of a boulder while bouldering, or the top of a climb while top roping.
 * tramming : A technique that is typically used while cleaning gear from a steep route. A quickdraw is clipped between the climber's harness and the rope that is threaded through the gear.  As the climber is lowered by the belayer, they will descend along the line of the gear.
 * traverse : To climb in a horizontal direction.
 * A feature of a route that allows relatively easy progress in a horizontal direction.
 * A Tyrolean traverse is crossing a chasm using a rope anchored at both ends.
 * A pendulum traverse involves swinging from a protection point.

 * tuber : A belay device.
 * tufa : A limestone formation, like a stalactite attached to the wall. e.g. "Mega Tufa Wall", Mallorca

U

 * undercling : A hold or flake that is upside down.

V

 * "V"-grade : A technical grading system for bouldering problems, invented by John Sherman.
 * verglas : A thin coating of ice that forms over rocks when rainfall or melting snow freezes on rock. Hard to climb on as crampons have insufficient depth for reliable penetration.

W

 * wand : A bamboo stick with a small flag on top used to mark paths over glaciers and snow fields.
 * webbing : Hollow and flat nylon strip, mainly used to make runners and slings.
 * weighting : As in, "weighting the rope." Any time the rope takes the weight of the climber. This can happen during a minor fall, a whipper (long fall), or simply by resting while hanging on the belay rope (see also hangdogging.)
 * whipper : A lead fall from above and to the side of the last clip, whipping oneself downwards and in an arc. Has come to be the term for any fall beyond the last placed or clipped piece of protection.
 * wired : To have the moves required for completing a climb memorized. See dialled.
 * wires : A slang term for nuts.
 * woodie : A home made climbing wall. Often specifically a hybrid between a climbing wall and a fingerboard. Specifically called such because of the wooden panels (usually left unpainted) used to attach the climbing holds to.

Y

 * Yosemite Decimal System : A numerical system for rating the difficulty of walks, hikes, and climbs in the United States. The rock climbing (5.x) portion of the scale is the most common climb grading system used in the US. The scale runs from 5.0 to 5.15a (as of 2005)

Z

 * Z-clipping : clipping into an anchor with the segment of rope from beneath the previous anchor, resulting in an unsafe configuration of the belay rope.
 * zipper fall : A fall in which each piece of protection fails in turn.
 * Z-pulley : A particular configuration of rope, anchors, and pulleys typically used to extricate a climber after falling into a crevasse.


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 * 1862: This figure is surrounded by a double border of golden rays following the same vesica outline, behind which the background is dispersed with starry circles. — The Times, 30 Aug 1862, p.10 col. F

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 * 1922: Stephen’s higher, more sibilant, who in the ultimate hours of the previous day had augmented by diuretic consumption an insistent vesical pressure. — James Joyce, Ulysses

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Talk:implement

Given its commonplace use, should the adjective "implementable" be included despite its historic absence from traditional print dictionaries?

RFV discussion
Has “Etymology: From Scottish English or Scots implement (“fulfill”)”

Unreferenced for one thing, and it doesn't look like a Scottish word to me, more like Latin. --Jerome Potts 03:35, 4 November 2011 (UTC)

 * You misunderstand the sentence. It is not Scottish Gaelic, it’s from Scots. English-speaking Scottish lawyers coined the word about 200 years ago for use in law with the meaning of to produce or cause fulfillment (as of a contract). It was a time when Classical education included lots of Latin and Greek. In Latin, the word was implementum (a filling up), from impleo (to fill). —Stephen (Talk) 03:58, 4 November 2011 (UTC)
 * Which definition is being disputed here? Mglovesfun (talk) 11:21, 4 November 2011 (UTC)

 * It is the Etymology 2 section (which currently relates only to implement (verb)) which was queried. FWIW, OED's first cite of implement (verb) is some legal-speak in Scotland in 1806, as Stephen says (OED doesn't differentiate between English English, Scottish English and Scots).  However, they also show (Scottish legal) use of implement (noun) to mean fulfilment from 1764 - 1868.

 * I suggest firstly, that the verbal use probably developed from that usage of the noun; secondly that that noun usage is not so very different from the Late Latin implementum (= a filling up); thirdly that the more common uses of implement (noun) are cited in OED from 1454, but with no obviously-Scottish English/Scots cites till after 1850, 80-odd years after the Scottish-legal use to mean fulfilment, by which time there had been much more cross-fertilisation between Scots and English English.

 * Since the Scottish legal meanings (both noun and verb) are much closer to the original Late Latin than any of the earlier English English meanings, it is strongly arguable that they came to English via Scots, rather than developing from the previous English usage...for which, unless someone finds a cite, there is no evidence of use in Scotland at that time.

 * So I would suggest keeping Etymology 2 separate from Etymology 1, but extending it to read "From Scottish English or Scots implement (“fulfill”), from Late Latin implēmentum (“a filling up”), from Latin impleō (“I fill up”)" thus noting it as a separate import. OED do not, and would not, make that distinction, because they treat Middle English, Scots and Modern English as one language, but since we do treat them separately, it is appropriate for us to do so.  Of course it would be great if someone could research old cites to add evidence to confirm this (unfortunately, I haven't time to research further myself at present) but with a meaning so much closer to the Late Latin than any of the English meanings, and since lawyers of the time would be familiar with Latin, it seems fairly sure.

 * I note that Semperblotto has already removed the RFV tag. I agree with Stephen and him, and if no one objects, in a day or two I shall extend the Etymology 2 as I proposed above. --Eng in ear 03:52, 5 November 2011 (UTC)

 * Yes, it does appear that Scottish lawyers "reinvented" the word with a slightly different meaning. The OED recognises the continuum from southern English to northern English to Scots, but since Scots now has the status of a separate language, and Scotland has always had separate laws, that proposal sounds reasonable.    D b f  i  r  s   21:30, 15 November 2011 (UTC)

 * Right then, struck. - -sche (discuss) 06:42, 18 March 2012 (UTC)

give tools to somebody (transitive); (law) requirement
Transitive: to provide or equip somebody with the tools or other means to do something (formal) (law) something needed in order to achieve something else (formal) --Backinstadiums (talk) 14:34, 11 September 2019 (UTC)

 * Noun: (LAW) 2. something needed in order to achieve something else (formal). JMGN (talk) 19:02, 30 June 2024 (UTC)

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Appendix:Glossary of game theory

This is a glossary of game theory—the branch of mathematics in which games are studied: that is, models describing human behaviour.

Notational conventions

 * real numbers : $$ \mathbb{R} $$.
 * The set of players : $$ \mathrm{N} $$.
 * strategy space : $$ \Sigma\ = \prod_{i \in \mathrm{N}} \Sigma\ ^i $$. Where:
 * player i's strategy space : $$ \Sigma\ ^i $$ is the space of all possible ways in which player i can play the game.
 * strategy for player i : $$ \sigma\ _i $$ is an element of $$ \Sigma\ $$.
 * complements : $$ \sigma\ _{ -i } $$ an element of $$ \Sigma\ ^{-i} = \prod_{ j \in \mathrm{N}, j \ne i} \Sigma\ ^j $$, is a tuple of strategies for all players other than i.
 * outcome space : $$ \Gamma\ $$ is in most textbooks identical to -
 * payoffs : $$ \mathbb{R} ^ \mathrm{N} $$, describing how much gain (money, pleasure, etc.) the players are allocated by the end of the game.

A

 * acceptable game : A game form such that for every possible preference profiles, the game has pure Nash equilibria, all of which are pareto efficient.

 * allocation of goods : A function $$ \nu\ : \Gamma\ \to \mathbb{R} ^\mathrm{N} $$. The allocation is a cardinal approach for determining the good (e.g. money) the players are granted under the different outcomes of the game.

B
\forall \sigma\ _i \in\ \Sigma\ ^i \quad \quad \pi\ (\sigma\ _i ,\sigma\ _{-i} ) \le \pi\ (\tau\ _i ,\sigma\ _{-i} ) $$.
 * best reply : The best reply to a given complement $$ \sigma\ _{-i} $$ is a strategy $$ \tau\ _i $$ that maximizes player i's payment. Formally, we want: $$

C

 * coalition : Any subset of the set of players: $$ \mathrm{S} \subseteq \mathrm{N} $$.

 * Condorcet winner : An outcome such that all non-dummy players prefer it to all other outcomes, given a preference ν on the outcome space.

 * cooperative game : A game in which players are allowed form coalitions (and to enforce coalitionary discipline). A cooperative game is given by stating a value for every coalition: $$ \nu\ : 2^{\mathbb{P}(N)} \to \mathbb{R}$$  It is always assumed that the empty coalition gains nil. Solution concepts for cooperative games usually assume that the players are forming the grand coalition $$ N $$, whose value $$ \nu(N) $$ is then divided among the players to give an allocation.

 * coordination game : A normal form game in which players have the same sets of strategies and their payoffs are higher if they chose the same strategies than they are if they choose different strategies.

D

 * dictator: A player is a strong dictator if he can guarantee any outcome regardless of the other players. $$m \in \mathbb{N}$$ is a weak dictator if he can guarantee any outcome, but his strategies for doing so might depend on the complement strategy vector. Naturally, every strong dictator is a weak dictator. Formally: m is a Strong dictator if: $$ \forall a \in \mathrm{A}, \; \exist \sigma\ _n \in \Sigma\ ^n \; s.t. \; \forall \sigma\ _{-n} \in \Sigma\ ^{-n}: \; \Gamma\ (\sigma\ _{-n},\sigma\ _n) = a $$ m is a Weak dictator if: $$ \forall a \in \mathrm{A}, \; \forall \sigma\ _{-n} \in \Sigma\ ^{-n} \; \exist \sigma\ _n \in \Sigma\ ^n \; s.t. \; \Gamma\ (\sigma\ _{-n},\sigma\ _n) = a $$  Another way to put it is: a weak dictator is $$\alpha$$-effective for every possible outcome. A strong dictator is $$\beta$$-effective for every possible outcome. See Effectiveness. Antonym: dummy.

\forall j \in \mathrm{N} \; \quad  \nu\ _j (a) \le\ \nu\ _j (b) $$ for domination, and $$ \exists i \in \mathrm{N} \; s.t. \; \nu\ _i (a)  <  \nu\ _i (b) $$ for strict domination. An outcome a is (strictly) dominated if it is (strictly) dominated by some other outcome. An outcome a is dominated for a coalition S if all players in S prefer some other outcome to a. See also Condorcet winner.
 * dominated outcome : Given a preference ν on the outcome space, we say that an outcome a is dominated by outcome b (hence, b is the dominant strategy) if it is preferred by all players. If, in addition, some player strictly prefers b over a, then we say that a is strictly dominated. Formally: $$

\forall \sigma\ _{-i} \in\ \Sigma\ ^{-i} \quad \quad \pi\ (\sigma\ _i ,\sigma\ _{-i} ) \le \pi\ (\tau\ _i ,\sigma\ _{-i} ) $$ and $$ \exists \sigma\ _{-i} \in\ \Sigma\ ^{-i} \quad s.t. \quad \pi\ (\sigma\ _i ,\sigma\ _{-i} ) < \pi\ (\tau\ _i ,\sigma\ _{-i} ) $$. A strategy σ is (strictly) dominated if it is (strictly) dominated by some other strategy.
 * dominated strategy : A strategy is (strongly) dominated by strategy $$ \tau\ _i $$ if for any complement strategies tuple $$ \sigma\ _{-i} $$, player i benefits by playing $$ \tau\ _i $$. Formally speaking: $$

 * dummy : A player i is a dummy if he has no effect on the outcome of the game. I.e. if the outcome of the game is insensitive to player i's strategy. Antonyms: say, veto, dictator.

E

 * effectiveness : A coalition (or a single player) S is effective for  a if it can force a to be the outcome of the game. S is α-effective if the members of S have strategies s.t. no matter what the complement of S does, the outcome will be a. S is β-effective if for any strategies of the complement of S, the members of S can answer with strategies that ensure outcome a.

 * extensive form game : A tree, where, at each node of the tree, a different player has the choice of choosing an edge.

F

 * finite game : A game with finitely many players, each of which has a finite set of strategies.

M

 * mixed strategy : For player i, a probability distribution P on $$ \Sigma\ ^i $$. It is understood that player i chooses a strategy randomly according to P.

 * mixed Nash equilibrium : Same as Pure Nash Equilibrium, defined on the space of mixed strategies. Every finite game has Mixed Nash Equilibria.

N

 * Nash equilibrium : The set of choices of players' strategies for which no player can benefit by changing his or her strategy while the other players keep theirs unchanged.

 * normal form game : A function: $$\Sigma\ ^ i \to \mathbb{R}^\mathrm{N}$$, given the tuple of strategies chosen by the players, one is given an allocation of payments (given as real numbers). A further generalization can be achieved by splitting the game into a composition of two functions: $$\Sigma\ ^i \to \Gamma\ $$ the outcome function of the game (some authors call this function "the game form"), and $$ \nu\ : \Gamma\ \to \mathbb{R}^\mathrm{N} $$ the allocation of payoffs (or preferences) to players, for each outcome of the game.

O

 * outcome function : A function that assigns to each combination of chosen strategies an outcome from an outcome space. It appears in one of the formalizations of a normal form game; see normal form game.

 * outcome space : A set of all the possible outcomes of a game—outcomes to which a real-valued award is assigned for each player. Conventionally labeled as $$\ \Gamma$$. It appears in one of the formalizations of a normal form game; see normal form game.

P

 * Pareto efficiency : The property of being Pareto efficient.

 * Pareto efficient : An outcome a of game form π is (strongly) Pareto efficient if it is undominated under all preference profiles.

 * Pareto optimal : Of an allocation of goods to individual, such that it is Pareto efficient.

 * Pareto optimal : Of a strategy of a player, such that there is no alternative strategy outperforming it agaist at least one opponent's strategy while not underperforming it against any opponent's strategy.

 * Pareto optimality : The property of being Pareto optimal.

 * payoff function : Informally, a mathematical function describing the real-valued award given to a single player at the outcome of a game. Formally, a function $$ F: \Sigma \rightarrow \mathbb{R} $$, where $$\Sigma$$ is the strategy space. Accordingly, to completely specify a game, the payoff function has to be specified for each player in the player set P= {1, 2, ..., m}.

 * preference profile : A real-valued function that specifies for each outcome of the game and each of N players to what degree he prefers the outcome; that is, $$ \nu\ : \Gamma\ \to \mathbb{R} ^\mathrm{N} $$, where $$\Gamma$$ is the outcome space. See allocation of goods. This is the ordinal approach at describing the outcome of the game.

\forall i \in \mathrm{N} \quad \forall \tau\ _i \in\ \Sigma\ ^i \quad \pi\ (\tau\ ,\sigma\ _{-i} ) \le \pi\ (\sigma\ ) $$. No equilibrium point is dominated.
 * pure Nash equilibrium point : An element $$ \sigma\ = \sigma\ _ {i \in \mathrm{N}} $$ of the strategy space of a game is a pure Nash equilibrium point if no player i can benefit by deviating from his strategy $$ \sigma\ _i $$, given that the other players are playing in $$ \sigma\ $$. Formally: $$

S

 * say : A player i has a Say if he is not a Dummy, i.e. if there is some tuple of complement strategies s.t. π (σ_i) is not a constant function. Antonym: dummy.

 * simple game : A simplified form of a cooperative game, where the possible gain is assumed to be eiter '0' or '1'. A simple game is couple (N, W), where W is the list of "winning" coalitions, capable of gaining the loot ('1'), and N is the set of players.

V

 * value : A value of a game is a rationally expected outcome. There are more than a few definitions of value, describing different meathods of obtaining a solution to the game.

 * veto : A veto denotes the ability (or right) of some player to prevent a specific alternative from being the outcome of the game. A player who has that ability is called a veto player. Antonym: dummy.

W

 * weakly acceptable game : A game that has pure Nash equilibria some of which are pareto efficient.

Z

 * zero-sum game : A normal form game for which, for each combination of strategies chosen by each player, the sum of the players' payoffs is zero.

title: Appendix:Glossary of game theory


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Appendix:Glossary of graph theory

This is a glossary of graph theory—a mathematical theory of graphs consisting of vertices and edges that connect vertices.

A

 * acyclic : Of graph, such one that it does not contain any directed cycle. A finite, acyclic digraph with no isolated vertices necessarily contain at least one source and at least one sink. See also directed acyclic graph (DAG for short) for more.

 * acyclic graph : A graph that contains no cycles.

 * adjacent : Two edges are adjacent if they have a node in common; two nodes are adjacent if they have an edge in common.

 * anti-edge : An edge that "is not there". More formally, for two vertices $$u$$ and $$v$$, $$\{u, v\}$$ is an anti-edge in a graph $$G$$ if $$(u, v)$$ is not an edge in $$G$$. This means that there is either no edge between the two vertices or there is only an edge $$(v, u)$$ from $$v$$ to $$u$$ if $$G$$ is directed.

 * anti-triangle : A set of three vertices none of which are connected.

 * arborescence : (also out-tree or branching) An oriented tree in which all vertices are reachable from a single vertex. Likewise, an in-tree is an oriented tree in which a single vertex is reachable from every other one.

 * adjacency matrix : In computers, a finite, directed or undirected graph (with n vertices, say) is often represented by its adjacency matrix: an n-by-n matrix whose entry in row i and column j gives the number of edges from the i-th to the j-th vertex.

 * adjacent : Two vertices u and v are considered adjacent if an edge exists between them. We denote this by u ↓ v. In the above graph, vertices 1 and 2 are adjacent, but vertices 2 and 4 are not. The set of neighbors, called a (open) neighborhood NG(v) for a vertex v in a graph G, consists of all vertices adjacent to v but not including v. When v is also included, it is called a closed neighborhood, denoted by NG[v]. When stated without any qualification, a neighborhood is assumed to be open. The subscript G is usually dropped when there is no danger of confusion. In the example graph, vertex 1 has two neighbors: vertices 2 and 5. For a simple graph, the number of neighbors that a vertex has coincides with its degree.

 * arc : (also directed edge) An ordered pair of endvertices.

 * articulation point : A cut vertex.

B

 * balanced k-partite graph : A k-partite graph such that each partite set differs in size by at most 1 with any other.

 * biclique : A complete bipartite graph.

 * biconnected component : A maximal set of edges in which any two members lie on a common simple cycle.

 * bipartite graph : A graph that can be decomposed into two partite sets but not fewer.

 * biregular graph : A graph that has unequal maximum and minimum degrees and every vertex has one of those two degrees.

 * block: Either a maximally 2-connected subgraph or a bridge with its endvertices.

 * bond : A minimal (but not necessarily minimum), nonempty set of edges whose removal disconnects a graph.

 * bridge : An edge whose removal disconnects a graph. (For example, a tree is made entirely of bridges.)

C

 * center : A vertex with minimum eccentricity.

 * circuit : A circuit of n vertices, denoted by Cn, is usually assumed to be a simple cycle, or a simple circuit, meaning that every vertex is incident to exactly two edges. In the above graph (1, 5, 2, 1) is a simple cycle.

 * circumference : The length of a longest (simple) cycle, or infinity if the graph is acyclic.

 * claw : An induced star with 3 edges.

 * clique : In a graph, a set of pairwise adjacent vertices. Since any subgraph induced by a clique is a complete subgraph, the two terms and their notations are usually used interchangeably.

 * k-clique : A clique of order k. In the example graph above, vertices 1, 2 and 5 form a 3-clique, or a triangle.

 * clique number : ω(G) of a graph G, the order of a largest clique in G.

 * color, colored, identified : Nodes or edges which are considered as individuals. Although they may actually be rendered in diagrams in different colors, working mathematicians generally pencil in numbers or letters.

 * k-colorable graph' : A graph that can be decomposed into k partite sets.

 * complement : $$\bar{G}$$ of a graph G is a graph with the same vertex set as G but with an edge set such that xy is an edge in $$\bar{G}$$ if and only if xy is not an edge in G.

 * complete : A graph in which every node is linked to every other node. For a complete digraph, this means one link in either direction.

 * complete graph : Kn of order n, a simple graph with n vertices in which every vertex is adjacent to every other. The example graph is not complete. The complete graph on n vertices is often denoted by Kn. It has n(n-1)/2 edges (corresponding to all possible choices of pairs of vertices).

 * complete multipartite graph : A graph in which vertices are adjacent if and only if they belong to different partite sets.

 * component : A maximally connected subgraph.

 * connected : If some route exists from every node to every other, the graph is connected. Note that some graphs are not connected. A diagram of an unconnected graph may look like two or more unrelated diagrams, but all the nodes and edges shown are considered as one graph.

 * connectivity : extends the concept of adjacency and is essentially a form (and measure) of concatenated adjacency.

 * connected graph : If it is possible to establish a path from any vertex to any other vertex of a graph, the graph is said to be connected.

 * k-connected : If it is always possible to establish a path from any vertex to every other one even after removing any k - 1 vertices, then the graph is said to be k-connected. Note that a graph is k-connected if and only if it contains k internally disjoint paths between any two vertices. The example graph above is connected (and therefore 1-connected), but not 2-connected.

 * connectivity : κ(G) of a graph G is the minimum number of vertices needed to disconnect G. By convention, Kn has connectivity n - 1; and a disconnected graph has connectivity 0.

 * crossing : A pair of intersecting edges.

 * crossing number : The minimum number of crossings that must appear when a graph is drawn on a plane is called the crossing number.

 * cut : A partition of the vertices of a graph into two disjoint subsets.

 * cut edge : A bridge.

 * cut set : A set of vertices whose removal disconnects the graph.

 * cut vertex : A vertex whose removal disconnects a graph. Also known as Cut Point or Articulation Point. See also cut set and bridge.

 * cycle : In a graph was a closed walk.

D

 * DAG : A directed acyclic graph.

 * degree : The number of edges which connect a node.

 * degree : dG(v) of a vertex v in a graph G is the number of edges incident to v, with loops being counted twice. A vertex of degree 0 is an isolated vertex. A vertex of degree 1 is a leaf. In the example graph vertices 1 and 3 have a degree of 2, vertices 2,4 and 5 have a degree of 3 and vertex 6 has a degree of 1. If E is finite, then the total sum of vertex degrees is equal to twice the number of edges.

 * degree sequence : A list of degrees of a graph in non-increasing order (e.g. d1 ≥ d2 ≥ … ≥ dn). A sequence of non-increasing integers is realizable if it is a degree sequence of some graph.

 * diagram : A visible rendering of the abstract concept of a graph.

 * diameter : The maximum eccentricity over all vertices in a graph. It is denoted diam(G) of a graph G.

 * digraph : A directed graph.

 * directed cycle : (also cycle) An oriented simple cycle such that all arcs go the same direction, meaning all vertices have in- and out-degrees 1.

 * directed : A graph in which each edge symbolizes an ordered, non-transitive relationship between two nodes. Such edges are rendered with an arrowhead at one end of a line or arc.

 * directed graph : A graph whose edges are directed, possibly represented as ordered pairs of vertices; synonyms: digraph. Alternative models of graph exist; e.g., a graph may be thought as a Boolean binary function over the set of vertices or as a square (0,1)-matrix.

 * disconnected graph : A graph that is not connected.

 * disconnecting set : A set of edges whose removal increases the number of components.

 * distance : dG(u, v) between two (not necessary distinct) vertices u and v in a graph G is the length of a shortest path between them. The subscript G is usually dropped when there is no danger of confusion. When u and v are identical, their distance is 0. When u and v are unreachable from each other, their distance is defined to be infinity ∞.

 * dominate : A vertex v dominates another vertex u if there is an arc from v to u. A vertex subset S is out-dominating if every vertex not in S is dominated by some vertex in S; and in-dominating if every vertex in S is dominated by some vertex not in S.

 * dominating set : Of a graph, a vertex subset whose closed neighborhood include all vertices of the graph. A vertex v dominates another vertex u if there is an edge from v to u. A vertex subset V dominates another vertex subset U if every vertex in U is adjacent to some vertex in V. The minimum size of a dominating set is the domination number γ(G).

 * dual : A dual, or planar dual when the context needs to be clarified, G* of a plane graph G is a graph whose vertices represent the faces, including any outerface, of G and are adjacent in G* if and only if their corresponding faces are adjacent in G. The dual of a planar graph is always a planar pseudograph (e.g. consider the dual of a triangle). In the familiar case of a 3-connected simple planar graph G (isomorphic to a convex polyhedron P), the dual G* is also a 3-connected simple planar graph (and isomorphic to the dual polyhedron P*).

E

 * eccentricity : εG(v) of a vertex v in a graph G is the maximum distance from v to any other vertex.

 * edge : A set of two elements, drawn as a line connecting two vertices, called endvertices, or endpoints. An edge with endvertices x and y is denoted by xy without any symbol in between, so, do not write x⋅y. The edge set of G is usually denoted by E(G), or E when there is no danger of confusion.

 * edge, link, arc : Relationships represented in a graph. These are always rendered as straight or curved lines. The term "arc" may be misleading.

 * edge cut : The set of all edges having one endvertex in some proper vertex subset S and another endvertex in V(G)\S. Edges of K3 form a disconnecting set but not an edge cut. Any two edges of K3 form a minimal disconnecting set as well as an edge cut. An edge cut is necessarily a disconnecting set; and a minimal disconnecting set of an nonempty graph is necessarily an edge cut.

 * edgeless graph : (empty graph) A graph possibly with some vertices, but no edges. Or, it is a graph with no vertices and no edges.

 * k-edge-connected : Of a graph, such that if any subgraph formed by removing any k - 1 edges is still connected. The edge connectivity κ′(G) of a graph G is the minimum number of edges needed to disconnect G. One well-known result is that κ(G) ≤ κ′(G) ≤ δ(G).

 * embeddable : A graph is embeddable on a surface if its vertices and edges can be arranged on it without any crossing. The genus of a graph is the lowest genus of any surface on which the graph can embed.

 * embedding : $$G_1 = (V_1,E_1)$$ of $$G_2 = (V_2,E_2)$$ is an injection from $$V_2$$ to $$V_1$$ such that every edge in $$E_2$$ corresponds to a path(disjoint from all other such paths) in $$G_1$$.

 * equipartite graph : A k-partite graph such that each partite set has the same size.

 * Eulerian circuit : Eulerian cycle.

 * Eulerian cycle : A closed walk which uses each edge precisely once.

 * Eulerian digraph : A digraph with equal in- and out-degrees at every vertex.

 * Eulerian path : A path which passes through every edge (once and only once). If the starting and ending nodes are the same, it is an Euler cycle or an Euler circuit. If the starting and ending nodes are different, it is an Euler trail.

 * Eulerian path : A graph is a walk that uses each edge precisely once; that is, a trail that uses all the edges. If such a trail exists, the graph is called traversable.

 * Eulerian trail : Eulerian path.

 * Eulerian tour : Eulerian cycle.

 * even cycle : A cycle that has an even length.

F

 * face : When a graph is drawn without any crossing, any cycle that surrounds a region without any edge reaching from the cycle inside to such region forms a face. Two faces on a plane graph are adjacent if they share a common edge.

 * factor : A spanning subgraph.

 * k-factor : A k-regular spanning subgraph. An 1-factor is a perfect matching. A partition of edges of a graph into k-factors is called a k-factorization. A k-factorable graph is a graph that admits a k-factorization.

 * forest : A vertex-disjoint union of trees; or, equivalently, an acyclic graph.

G

 * girth : Of a graph, the length of a shortest (simple) cycle in the graph, or infinity if the graph is acyclic.

 * graph, network : An abstraction of relationships among objects. Graphs consist exclusively of nodes and edges. All characteristics of a system are either eliminated or subsumed into these elements.

 * graph : A mathematical structure costiting of two types of elements, namely vertices and edges. Every edge has two endpoints in the set of vertices, ans is said to connect or join the two endpoints. The set of edges can thus be defined as a subset of the family of all two-element sets of vertices. Often, however, the set of vertices is considered as a set, and there is an incidence relation which maps each edge to the pair of vertices that are its endpoints.

 * graph invariant : A property of a graph G, usually a number or a polynomial, that depends only on the isomorphism class of G; examples are genus and graph order.

 * graph labeling : The assignment of unique labels (usually natural numbers) to the edges and vertices of a graph. Graphs with labeled edges or vertices are known as labeled, those without as unlabeled. More specifically, graphs with labeled vertices only are vertex-labeled, those with labeled edges only are edge-labeled. (This usage is to distinguish between graphs with identifiable vertex or edge sets on the one hand, and isomorphism types or classes of graphs on the other.)

H

 * Hamiltonian cycle : A spanning cycle.

 * Hamiltonian graph : A graph that contains a Hamiltonian cycle.

 * Hamiltonian path : A (simple) path that contains every vertex.

 * Hamiltonian path : A path which passes through every node once and only once. If the starting and ending nodes are adjacent, it is a Hamiltonian cycle.

 * Hamiltonian path : A spanning path.

 * Hamiltonian connected graph : A graph that, given any pair of (distinct) vertices, contains a Hamiltonian path using them as endvertices.

 * H-free graf : A graph that does not contain H as an induced subgraph is said to be H-free.

 * head : The first vertex in the arc AKA directed edge. See also tail.

 * homomorphic : Likewise, a graph G is said to be homomorphic  to a graph H if there is a mapping, called a homomorphism, from V(G) to V(H) such that if two vertices are adjacent in G then their corresponding vertices are adjacent in H.

 * hyperedge : An edge that is allowed to take on any number of vertices, possibly more than 2. A graph that allows any hyperedge is called a hypergraph. A simple graph can be considered a special case of the hypergraph, namely the 2-uniform hypergraph. However, when stated without any qualification, an edge is always assumed to consist of at most 2 vertices, and a graph is never confused with a hypergraph.

I

 * in degree : The number of edges entering a vertex. Is denoted as dΓ-(v). The degree dΓ(v) of a vertex v is equal to the sum of its out- and in- degrees. When the context is clear, the subscript Γ can be dropped. Maximum and minimum out degrees are denoted by Δ+(Γ) and δ+(Γ); and maximum and minimum in degrees, Δ-(Γ) and δ-(Γ).
 * in-neighborhood : (predecessor set) N-Γ(v) of a vertex v is the set of heads of arc going into v.

 * incident : An edgee connects two vertices; these two vertices are said to be incident to that edge, or, equivalently, that edge incident to those two vertices. All degree-related concepts have to do with adjacency or incidence.

 * independence number : α(G) of a graph G is the size of a largest independent set of G.

 * independent : In graph theory, the word independent usually carries the connotation of pairwise disjoint or mutually nonadjacent. In this sense, independence is a form of immediate nonadjacency.

 * independent set : A set of isolated vertices. Since the graph induced by any independent set is an empty graph, the two terms are usually used interchangeably. In the example above, vertices 1, 3, and 6 form an independent set; and 3, 5, and 6 form another one.

 * induced subgraph : A subgraph H of a graph G is said to be induced if, for any pair of vertices x and y of H, xy is an edge of H if and only if xy is an edge of G. In other words, H is an induced subgraph of G if it has the most edges that appear in G over the same vertex set. If H is chosen based on a vertex subset S of V(G), then H can be written as G[S] and is said to be induced by S.

 * infinite : A graph is infinite if it has infinitely many vertices or edges or both; otherwise the graph is finite. An infinite graph where every vertex has finite degree is called locally finite. When stated without any qualification, a graph is usually assumed to be finite.

 * initial vertex : A head.

 * internally disjoint : Two paths are internally disjoint (some people call it independent) if they do not have any vertex in common, except the first and last ones.

 * isolated vertex : A vertex not incident to any edges.

 * isomorphic : Two graphs G and H are said to be isomorphic, denoted by G ~ H, if there is a one-to-one correspondence, called an isomorphism, between the vertices of the graph such that two vertices are adjacent in G if and only if their corresponding vertices are adjacent in H.

 * isthmus : A bridge.

K

 * k-ary tree : A k-ary tree is a rooted tree in which every internal vertex has k children. An 1-ary tree is just a path. A 2-ary tree is also called a binary tree.

 * kernel : An independent out-dominating set. A digraph is kernel perfect if every induced sub-digraph has a kernel.

 * knot : In a directed graph, a collection of vertices and edges with the property that every vertex in the knot has outgoing edges, and all outgoing edges from vertices in the knot have other vertices in the knot as destinations. Thus it is impossible to leave the knot while following the directions of the edges.

L

 * length of a cycle : The number of its edges. Cn has length n. A cycle, unlike a path, is not allowed to have length 0.

 * length of a path or walk : The number of edges that the path uses. Pn has length n - 1. Some people count multiple edges multiple times. In the example graph, (1, 2, 5, 1, 2, 3) is a path with length 5, and (5, 2, 1) is a simple path of length 2.

 * link : has two distinct endvertices.

 * digon : A cycle of length 2. In the example graph, (1, 2, 3, 4, 5, 1) is a cycle of length 5.

 * loop : An edge whose endvertices are the same vertex.

 * loop, cycle : A path which ends at the node where it began.

M

 * matching number : α′(G) of a graph G is a the size of a largest matching, or pairwise vertex disjoint edges, of G.

 * maximum degree : Δ(G) of a graph G, the largest degree over all vertices; the minimum degree δ(G), the smallest.

 * minor : $$G_2 = (V_2,E_2)$$ of $$G_1 = (V_1,E_1)$$ is an injection from $$V_2$$ to $$V_1$$ such that every edge in $$E_2$$ corresponds to a path(disjoint from all other such paths) in $$G_1$$ such that every vertex in $$V_1$$ is in one or more paths, or is part of the injection from $$V_1$$ to $$V_2$$. This can alternatively be phrased in terms of contractions, which are operations which collapse a path and all vertices on it into a single edge (see edge contraction).

 * multiple: A set of arcs are multiple, or parallel, if they share the same head and the same tail. A pair of arcs are anti-parallel if one's head/tail is the other's tail/head.

 * multiple edge: An edge such that there is another edge with the same endvertices; antonyms: simple edge. The multiplicity of an edge is the number of multiple edges sharing the same endvertices; the multiplicity of a graph, the maximum multiplicity of its edges.

 * multigraph : A graph that has multiple edges, but no loops.

 * multipartite graph : A graph that can be decomposed into an unspecific number of partite sets but not fewer.

N

 * network : A weighted graph, possibly directed or undirected, possibly containing special vertices (nodes), such as source or sink.

 * null graph : The graph with no vertices and no edges. Or, it is a graph with no edges and any number $$n$$ of vertices, in which case it may be called the null graph on $$n$$ vertices. (There is no consistency at all in the literature.)

O

 * odd cycle : A cycle that has odd length.

 * order : The order of a graph is the number of its vertices, i.e. |V(G)|.

 * orientation : An assignment of directions to the edges of an undirected or partially directed graph. When stated without any qualification, it is usually assumed that all undirected edges are replaced by a directed one in an orientation. Also, the underlying graph is usually assumed to be undirected and simple.

 * oriented graph : A graph that contains only arcs. When stated without any qualification, a graph is almost always assumed to be undirected. Also, a digraph is usually assumed to contain no undirected edges.

 * out degree : The number of edges leaving a vertex. Is denoted dΓ+(v), given a digraph Γ. See also in degree.

 * out-neighborhood : (successor set) N+Γ(v) of a vertex v is the set of tails of arcs going from v.

 * outer face : Furthermore, since we can establish a sense of "inside" and "outside" on a plane, we can identify an "outermost" region that contains the entire graph if the graph does not cover the entire plane. Such outermost region is called an outer face.

 * outerplanar graph : A graph that can be drawn in the planar fashion such that its vertices are all adjacent to the outer face. See also outerplane graph.

 * outerplane graph : A graph that is drawn in the planar fashion such that its vertices are all adjacent to the outer face. See also outerplanar graph.

P

 * pancyclic graph : A graph that contains cycles of every possible length (from 3 to the order of the graph).

 * k-partite graph : A graph that can be decomposed into k partite sets but not fewer.

 * partite set : A graph can be decomposed into independent sets in the sense that the entire vertex set of the graph can be partitioned into pairwise disjoint independent subsets. Such independent subsets are called partite sets, or simply parts.

 * path : A directed path, or just a path when the context is clear, is an oriented simple path such that all arcs go the same direction, meaning all internal vertices have in- and out-degrees 1.

 * path : A route that does not pass any edge more than once. If the path does not pass any node more than once, it is a simple path.

 * path : In a graph was what is now usually known as an open walk. Nowadays, when stated without any qualification, a path of n vertices, denoted by Pn (but some write Pn-1), is usually defined to be a simple path or a simple trail in the old sense, meaning that every vertex is incident to at most two edges.

 * perfect matching : A spanning matching.

 * peripheral vertex : A vertex with maximum eccentricity.

 * planar graph : A graph that can be drawn on the (Euclidean) plane without any crossing; a graph of genus 0.

 * plane graph : A graph that is drawn on the (Euclidean) plane without any crossing.

 * point, node, vertex : Objects ("things") represented in a graph. These are almost always rendered as round dots.

 * k-th power : Gk of a graph G is a supergraph formed by adding an edge between all pairs of vertices of G with distance at most k. A second power of a graph is also called a square.

 * pseudograph : A graph that contains both multiple edges and loops (the literature is highly inconsistent).

R

 * radius : The minimum eccentricity over all vertices in a graph. It is denoted rad(G) of a graph G. When there are two components in G, diam(G) and rad(G) defined to be infinity ∞.

 * reachable : Of a vertex v from a given vertex u in a directed graph, such that there is a directed path that starts from u and ends at v.

 * regular : A graph in which each node has the same degree.

 * regular graph : A graph in which every vertex has the same degree.

 * k-regular graph: A graph in which every vertex has degree k. A 0-regular graph is an independent set. A 1-regular graph is a matching. A 2-regular graph is a vertex disjoint union of cycles. A 3-regular graph is said to be cubic, or trivalent.

 * route : A sequence of edges and nodes from one node to another. Any given edge or node might be used more than once.

S

 * separating set : A cut set.

 * simple : A digraph is called simple if it has no loops and at most one arc between any pair of vertices. When stated without any qualification, a digraph is usually assumed to be simple.

 * simple graph : A graph that has no multiple edges or loops. When stated without any qualification, a graph is almost always assumed to be simple. See also multigraph.

 * sink : A vertex of a network with out-degree of zero; see also source.

 * size of a graph : The number of its edges, i.e. |E(G)|.

 * source : A vertex of a network with in-degree of zero; see also sink.

 * k-spanner : A spanning subgraph in which every two vertices are at most k times as far apart on S than on G. The number k is the dilation. k-spanner is used for studying geometric network optimization.

 * spanning subgraph : A subgraph H of a graph G such that it has the same vertex set as G. We say H spans G.

 * spanning tree : A spanning subgraph that is a tree. Every graph has a spanning forest. But only a connected graph has a spanning tree.

 * star : A special kind of tree called star is K1,k; see also claw.

 * strongly connected : A digraph is strongly connected if every vertex is reachable from every other following the directions of the arcs. On the contrary, a diagraph is weakly connected if its underlying undirected graph is connected. A weakly connected graph can be thought of as a digraph in which every vertex is "reachable" from every other but not necessarily following the directions of the arcs. A strong orientation is an orientation that produces a strongly connected digraph.

 * strongly connected component : Informally, a subgraph where all nodes in the subgraph are reachable by all other nodes in the subgraph.

 * subtree : of the graph G is a subgraph that is a tree.

 * subgraph : Of a graph G is a graph whose vertex and edge sets are subsets of those of G. In the other direction, a supergraph of a graph G is a graph that contains G as a subgraph. We say a graph G contains another graph H if some subgraph of G is H or is isomorphic to H (depending on the needs of the situation).

 * semiregular : A k-partite graph is semiregular if each of its partite set has a uniform degree

 * spanning matching : A matching that covers all vertices of a graph.

 * stable set : An independent set.

 * staset : A stable set.

 * strongly regular graph : A regular graph such that any adjacent vertices have the same number of common neighbors as other adjacent pairs and that any nonadjacent vertices have the same number of common neighbors as other nonadjacent pairs.

T

 * tail : The second vertex in the arc AKA directed edge. See also head.

 * terminal vertex : tail.

 * theta graph : The union of three internally disjoint (simple) paths that have the same two distinct endvertices. A theta0 graph has seven vertices which can be arranged as the vertices of a regular hexagon plus an additional vertex in the center. The eight edges are the perimeter of the hexagon plus one diameter.

 * thickness : The minimum number of planar graphs needed to cover a graph is the thickness of the graph.

 * totally disconnected graph : A graph is totally disconnected if there is no path connecting any pair of vertices. This is just another name to describe an empty graph or independent set.

 * tournament : A digraph in which each pair of vertices is connected by exactly one arc. In other words, it is an oriented complete graph.

 * traceable graph : A graph that contains a Hamiltonian path.

 * traceable path : A spanning path.

 * trail : A walk in which all the edges are distinct. (A closed trail has been called a tour or circuit, but these are uncommon and the latter is usually reserved for a regular subgraph of degree two.)

 * tree : A connected graph with no loops.

 * tree : A connected acyclic simple graph. A vertex of degree 1 is called a leaf, or pendant vertex. An edge incident to a leaf is an leaf edge, or pendant edge. (Some people define a leaf edge as a leaf and then define a leaf vertex on top of it. These two sets of definitions are often used interchangeably.) A non-leaf vertex is an internal vertex. Sometimes, one vertex of the tree is distinguished, and called the root. A rooted tree is a tree with a root. Rooted trees are often treated as directed acyclic graphs with the edges pointing away from the root. Trees are commonly used as data structures in computer science (see tree data structure).

 * triangle : C3 is called a triangle.

 * tripartite graph : A graph that can be decomposed into three partite sets but not fewer.

U

 * undirected edge : An edge that disregards any sense of direction and treats both endvertices interchangeably.

 * undirected : A graph in which each edge symbolizes an unordered, transitive relationship between two nodes. Such edges are rendered as plain lines or arcs.

 * unicyclic graph : A graph that contains exactly one cycle.

 * unidentified : Nodes or edges which are not considered as individuals. Only the way in which they connect to the rest of the graph characterize unidentified nodes and edges.

 * universal graph : In a class K of graphs, a simple graph in which every element in K can be embedded as a subgraph.

 * unweighted : A graph in which all the relationships symbolized by edges are considered equivalent. Such edges are rendered as plain lines or arcs.

V

 * valency : A degree.

 * vertex : A basic element of a graph, drawn as a node or a dot. The vertex set of G is usually denoted by V(G), or V when there is no danger of confusion.

 * vertex cut : A cut set.

W

 * walk : An alternating sequence of vertices and edges, beginning and ending with a vertex, in which each vertex is incident to the two edges that precede and follow it in the sequence, and the vertices that precede and follow an edge are the endvertices of that edge. A walk is closed if its first and last vertices are the same, and open if they are different.

 * weighted : Weighted edges symbolize relationships between nodes which are considered to have some value, for instance, distance or lag time. Such edges are usually annotated by a number or letter placed beside the edge. Weighted nodes also have some value; this must be distinguished from identification.

 * weighted graph : A graph that associates a label (weight) with every edge in the graph. Weights are usually real numbers. They may be restricted to rational numbers or integers. Certain algorithms require further restrictions on weights; for instance, the Dijkstra algorithm works properly only for positive weights.

 * weight of a subgraph: The sum of the weights of the edges of the subgraph.

 * Wiener index of a vertex : v in a graph G, denoted by WG(v) is the sum of distances between v and all others.

 * Wiener index of a graph : G, denoted by W(G), is the sum of distances over all pairs of vertices.

 * Wiener polynomial of an undirected graph : Σ qd(u,v) over all unordered pairs of vertices u and v.

title: Appendix:Glossary of graph theory


text:
Appendix:Glossary of group theory

This is a glossary of group theory. Throughout the article, we use e to denote the identity element of a group.

A

 * abelian group : A group $$(G,*)$$ is abelian if $$*$$ is commutative, i.e. $$g*h = h*g$$ for all $$g,h \in G$$. Likewise, a group is nonabelian if this relation fails to hold for any pair $$g,h \in G$$.

C

 * coset : If $$G$$ is a group, and $$H$$ is a subgroup of $$G$$, and $$g$$ is an element of $$G$$, then gH = { gh : h ∈ H } is the left coset of H in G with respect to g, and Hg = { hg : h ∈ H } is the right coset of H in G with respect to g.

D

 * direct product : direct sum, and semidirect product of groups. These are ways of combining groups to construct new groups; please refer to the corresponding links for explanation.

F

 * factor group : Or quotient group. Given a group G and a normal subgroup N of G, the quotient group is the set G/N of left cosets {aN : a∈G} together with the operation aN*bN=abN. The relationship between normal subgroups, homomorphisms, and factor groups is summed up in the fundamental theorem on homomorphisms.

 * finitely generated group : If there exists a finite set S such that  = G, then G is said to be finitely generated. If S can be taken to have just one element, G is a cyclic group of finite order, an infinite cyclic group, or possibly a group {e} with just one element.

 * free group : Given any set A, one can define a multiplication of words as follows: (abb)*(bca)=abbbca. The free group generated by A is the smallest group containing this semigroup.

G

 * general linear group : Denoted by GL(n, F), is the group of n-by-n invertible matrices, where the elements of the matrices are taken from a field F such as the real numbers or the complex numbers.

 * group : A set together with an associative operation which admits an identity element and such that every element has an inverse.

 * group isomorphism : Group homomorphisms that have inverse functions. The inverse of an isomorphism, it turns out, must also be a homomorphism.

 * group homomorphism : These are functions f : (G,*) → (H,×) that have the special property that f(a * b) = f(a) × f(b) for any elements a and b of G.

 * group representation : (not to be confused with the presentation of a group). A homomorphism from a group to a general linear group. One basically tries to "represent" a given abstract group as a concrete group of invertible matrices which is much easier to study.

I

 * isomorphic groups : Two groups are isomorphic if there exists a group isomorphism mapping from one to the other. Isomorphic groups can be thought of as essentially the same, only with different labels on the individual elements.

K

 * kernel : Given a group homomorphism, the preimage of the identity in the codomain of the group homomorphism. Every normal subgroup is the kernel of a group homomorphism and vice versa.

N

 * normal subgroup : H is a normal subgroup of G if for all g in G and h in H, g * h * g−1 also belongs to H.

O

 * order : Of a group $$(G, *)$$, the cardinality (i.e. number of elements) of $$G$$. (A group with finite order is called a finite group.)

 * order : Of an element of a group. Suppose $$x \in G$$ and there exists a positive integer $$m$$ such that $$x^m = e$$, then the smallest possible $$m$$ is called the order of $$x$$. The order of a finite group is divisible by the order of every element.

P

 * p-group : If p is prime, then a p-group is a group G where for each element g∈G, there exists a positive integer m such that the order of g is pm. A finite group is a p-group if and only if its group order (i.e. the number of its elements) is itself a power of p.

 * p-subgroup : A subgroup which is also p-group. (The study of p-subgroups is the central object of the Sylow theorems.)

S

 * simple group : Simple groups are those groups with {e} and itself as the only normal subgroups. The name is misleading as its structure could be extremely complex.  An example is the monster group, a group of order more than one million.  Every finite group is built up from simple groups through the use of group extensions, so the study and classification of finite simple groups is central to the study of finite groups in general. As a result of extensive effort over the second half of the 20th century, the finite simple groups have all been.

 * subgroup : Given group (G,*), a subset H which remains a group when the operation * is restricted to H. Given a set S of G. We denote by  the smallest subgroup of G containing S.

title: Appendix:Glossary of group theory


text:
rantaviiva

Noun

 * 1) shoreline
 * 2) coastline

title: rantaviiva


text:
نسر

Etymology 1
From, whence was derived the denominal root.

Noun

 * 1)  a vulture
 * 2)  an eagle

Usage notes
The word is commonly used to refer to eagles, especially in the dialects. This use, however, is almost unanimously criticized by prescriptivists, who maintain that should be used instead.

Verb

 * 1) to cut, pierce, or slit, especially like a vulture or another bird of prey
 * 2) to pluck
 * 3)  to bad-mouth, to malign, to abuse verbally, to slander, to slur
 * 1)  to bad-mouth, to malign, to abuse verbally, to slander, to slur
 * 1)  to bad-mouth, to malign, to abuse verbally, to slander, to slur

Verb

 * 1) to rip or tear

Etymology
From.

Noun

 * 1) an eagle

Etymology
.

Noun

 * 1) vulture
 * 2) eagle
 * 1) eagle

Etymology
From.

Noun

 * 1) eagle
 * 2) vulture

title: نسر


text:
Appendix:Japanese tea ceremony terms

This is an alphabetical list of terms used in Japanese tea ceremony. Note that in tea ceremony terms are often prefixed with the Japanese honorifics "o-" or "go"; terms are listed here under the first letter of the word (eg: kama), followed by the honorific, if applicable (o-kama).

C

 * Cha, o-cha
 * Tea; tea ceremony; the study of tea.

 * Cha-ire, o-cha-ire
 * A general term for containers, usually ceramic, made for holding thick tea. See Chaki.

 * Chajin
 * A person who studies tea; a tea master.

 * Chaki
 * Tea caddy; container for holding powdered green tea. See also: Cha-ire, Natsume.

 * Chakin
 * A white hemp or linen cloth used for handling hot lids and for the ritual cleaning of tea implements during tea ceremonies.

 * Chakin tarai
 * A bowl, usually made from copper, used for rinsing and washing chakin. It is kept on the bamboo sink-covering in the mizuya.

 * Chamei, o-chamei
 * The name of a batch of tea; a tea name. A tea name is a name given to advanced practitioners of tea ceremony, by which they are known in the tea world.  Tea names are usually chosen by the iemoto and are bestowed during a formal ceremony.  The name of every member of a given school will usually have at least one Chinese character in common.

 * Charcoal
 * See Sumi.

 * Chasen
 * A whisk hand carved from bamboo, used to blend powdered tea and water.

 * Chasen kusenaoshi
 * A whisk shaper, used to restore or maintain the shape of chasen.

 * Chashaku, o-chashaku
 * A tea scoop carved from bamboo.

 * Chashitsu
 * Tea house, tea room.

 * Chawan, o-chawan
 * A bowl for drinking tea.

D

 * Dōgu
 * equipment for tea ceremony

F

 * Fuku, puku
 * The counter for bowls of tea. See also: Fukukagen.

 * Fukukagen, o-fukukagen
 * A bowl of tea; a serving of tea.

 * Fukusa
 * A square, silk cloth used for ritual cleaning of tea equipment and for handling hot lids. See also: Kobukusa.

I

 * Iemoto, o-iemoto
 * The head of a tea school; the founder of a tea school.

K

 * Kama, o-kama
 * An iron pot used for heating water during tea ceremonies.

 * Kensui
 * A waste-water container used by the host in the tea room during ceremonies. Water that has been used to rinse the tea bowl is emptied into the bowl, and in the event that the host must dispose of a small item (such as a used sheet of kaishi), he or she will place it in the kensui. Since it is considered dirty, kensui is kept out of sight of the guests as much as possible. It is the last item brought into the tea room, and the first item removed.

 * Kobukusa
 * A small fukusa used for handling tea implements.

M

 * Matcha
 * Powdered green tea.

 * Mizusashi
 * A fresh water container used by the host in the tea room during ceremonies. The water it holds, which is cool, is used to rinse implements during the ritual cleaning, as well as to replenish the water in the kama at the end of certain ceremonies.

 * Mizutsugi
 * A pot with a spout, resembling a large teapot. It holds fresh, cool water, and is used to replenish the water in the kama or tetsubin at the end of certain ceremonies. The mizusashi is not kept in the tea room, but rather is brought in as the final step of certain ceremonies for the purpose of replenishing the pot.

 * Mizuya
 * Preparation area. A separate room or a small area where the host gathers and prepares the equipment and supplies needed for a tea ceremony.

 * Mushanokōjisenke
 * One of the three main Schools of Japanese tea ceremony descended from Sen no Rikyu, and one of the so-called san senke. The other two are Urasenke and Omotesenke.

O

 * Omotesenke
 * One of the three main schools of tea ceremony descended from Sen no Rikyu, and one of the so-called san senke. The other two are Urasenke and Mushanokōjisenke.

R

 * Raku
 * The name of a kiln and a style of creating pottery and tea bowls used in tea ceremony.

S

 * Shifuku, o-shifuku
 * A bag, usually silk, made for holding tea utensils. Certain utensils are always placed in shifuku, such as cha-ire.

 * Sumi
 * Charcoal. Both ro and furo were traditionally heated with charcoal, but now electric versions are available.  Charcoal is still preferred on formal occasions, however.

T

 * Tea caddy
 * See Cha-ire, Chaki, Koi-chaki, Natsume, Usu-chaki.

 * Temae
 * Tea ceremony procedure.

 * Tetsubin
 * An iron teapot-shaped pot used for heating water (but not brewing tea) during tea ceremonies.

 * Tokonoma
 * The scroll alcove in a tea room, where scrolls are hung and other decorations are placed.

U

 * Urasenke
 * One of the three main schools of tea ceremony descended from Sen no Rikyu, and one of the so-called san senke. The other two are Mushanokōjisenke and Omotesenke.

title: Appendix:Japanese tea ceremony terms


text:
نجمة

Noun

 * 1) star
 * 2) asterisk
 * 3) movie star, star performer

Etymology
From.

Noun

 * 1) star
 * 2) movie star, star performer

Etymology
From.

Noun

 * 1) star
 * 2) asterisk

title: نجمة


text:
rannikko

Noun

 * 1) coast

Etymology
From.

Noun

 * 1) coast

title: rannikko