xxyxyy the catalan numbers other applications
{"Image DocumentName": "X X Y X Y Y ( ( ) ( ) ) The Catalan Numbers Other applications:", "Image ImageDescription": "We could replace the X\u2019s by opening brackets and Y\u2019s by closing brackets. Thus, the Catalan numbers also give us the number of possible valid bracketings. Other applications: The number of binary trees with n+1 leaves (binary meaning that each parent has 2 children): The number of ways a convex polygon with \ud835\udc5b+2 sides can be cut into triangles: Problem 4 on Worksheet 3 (involving non-overlapping handshakes across a table) also yields the Catalan numbers!", "Image XResolution": "300", "Image YResolution": "300", "Image ResolutionUnit": "Pixels/Inch", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}