## Tagged Questions

0answers
99 views

### One element not belong to at least half of the subsets [closed]

Let $F$ be a collection of subsets of a finite set that is closed under intersection (meaning that the empty set is an element of $F$). Is it true that there must exist one element …
1answer
97 views

### General and translational Birkhoff lattices. Equational classes.

By  lattice  I'll mean  Birkhoff lattice. The two classical equational classes of lattices are modular lattices and distributive lattices. The old problem used to b …
6answers
1k views

### Show that this ratio of factorials is always an integer

show the formula always gives an integer $$\frac{(2m)!(2n)!}{m!n!(m+n)!}$$ I don't remember where I read this problem, but it said this can be proved using a simple counting argu …
0answers
275 views

### Reference/quote request: “All of combinatorics is the representation theory of $S_n$”

I think I remember reading somewhere a glib (or is it deep?) quote, perhaps due to Rota?, which was something like "All of combinatorics is essentially [or can be reduced to?] …
0answers
92 views

### An interesting version of the problem “balls into bins”

Consider n people, each has k identical balls. Each people choose k different bins from m bins, constrained by the condition that there are no two people choose exactly the same k …
1answer
221 views

### Is there a name for this graph?

I'm trying to find out whether the following graph has a name: Let $W$ be an $n$-dimensional vector space over $GF(q)$. The vertices of the graph are all the subspaces of $W$. Two …
0answers
43 views

### Approximate closed-form solution for a recurrence

Find an (approximate) closed-form solution for $S(m, b)$. S(m,b)=\sum_{i=0}^{\lfloor (e-1)/2\rfloor}{e \choose i}S(m-1, b-i) \quad + \sum_{i=\lfloor (e-1)/2\rfloor+1}^{\ …
1answer
325 views

### Enumerating/counting paths of a given length on a 2D lattice

All, I'm wondering if anyone can point me to a reference on how to address the following problem. In my thesis work on lattice QCD many years ago I had to enumerate all possible …
0answers
83 views

### A detail in the proof of the Motzkin-Straus theorem

The Motzkin-Straus theorem says that the global optimum of the quadratic program $$\max f(x)=\frac{1}{2} x^{t}Ax,\qquad \mbox{ subject to }\sum x_{i}=1 \mbox{ and } x_{i}\geq 0,$$ …
1answer
91 views

### The distribution of cycle length in random derangement

It is known that for a fixed x $\in {0,1,...,N-1}$, the length of the cycle of x in a random permutation in $S_N$ distributes uniformly in ${1, . . . ,N}$. My question is regardin …
4answers
1k views

### Verifying the correctness of a Sudoku solution

A Sudoku is solved correctly, if all columns, all rows and all 9 subsquares are filled with the numbers 1 to 9 without repetition. Hence, in order to verify if a (correct) solution …
2answers
80 views

### Incidence matrices of generalized quadrangles

Is there somewhere a database of incidence matrices of generalized quadrangles that one can download?
2answers
173 views

### Discrete disjoint covering of integer lattices

Is there a covering of $\mathbb{Z}^n$ by disjoint translates of the basis-and-origin minimal integer $n$-simplex? By haphazard I have such coverings for $\mathbb{Z}$, \$\mathbb{Z}^2 …
0answers
212 views

### Example of a group with unsolvable word problem

Today I noticed that the last relator in the 27-relator presentation of a group with unsolvable word problem given in Donald J. Collins: A simple presentation of a group with u …
0answers
127 views
+150

### Checking whether an element is in all inclusion-wise maximal common independent sets of two matroids

Given two matroids $M$ and $M'$ over the same universe $E$, and some element $x \in E$, I am interested in the importance of $x$ for the intersection (the common independent sets) …

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