Mathematics Problem Archive

A spanning tree of a graph G is called $\epsilon$-thin if it contains at most an $\epsilon$ fraction of the edges of each cut. Is there a function $f:...

Let $M$ be a matroid of rank n whose ground set S can be partitioned into n disjoint bases $B_1,\dots,B_n$. Is it true that $B_1,\dots,B_n$ always hav...

For positive integers $N,q,a$, let $Q(N;q,a)$ be the number of perfect squares among $a,a+q,\ldots,a+(N-1)q$, and let $Q(N)=\max_{q,a\geq1}Q(N;q,a)$. ...

Let $M(n)$ be the number of monotone Boolean functions of $n$ variables, equivalently the number of antichains of subsets of an $n$-element set. Deter...