All Questions

It is well known that for a bipartite graph $G$ with bi-adjacency matrix $A$, then $\det A \neq 0$ (as a polynomial) iff $G$ has a perfect matching (there is a similar result for general graphs with ...

Given an $m\times n$ chess board, we place $p$ $2\times 1$ dominoes on the board so that they don't overlap. How many ways can we place them? When each square of the board is covered by a domino this ...

Given $s>t\ge 2$, let $N(s,t)$ be the smallest integer $n>s$ such that there exists an “$(n;s;t;1)$-design” (i.e., a collection of $s$-subsets $e_1,\dots,e_m$ of $[n]:=\{1,\dots,n\}$, such that ...

A resolution (in the combinatorial design sense) of $K_{n}$ is a collection of sets of edges of $K_{n}$ so that within each set of edges, each vertex appears once, and over the entire collection, each ...

Let $p<1$ be a constant. Consider two sets $A,B$, each with $n$ vertices. For each pair $(a,b)\in A\times B$, the edge between $a$ and $b$ appears with probability $p$, independently of the ...

Imagine a number of chords of a sphere $S$ which nearly, but not quite, pass through the center of $S$, in such a way that no pair of chords intersect:       I would like to ...