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 …

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 …

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 …

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?] …

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 …

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 …

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}^{\ …

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 …

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

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 …

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 …

Is there somewhere a database of incidence matrices of generalized quadrangles that one can download?

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 …

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 …

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) …