Joy Cooper

A Latin square of order $n$ is an $n\times n$ grid of $n$ symbols each appearing exactly once in every row and column. If we decompose Latin squares by symbol, we can express them as sums of permutation matrices equalling a constant matrix. In this...

Given a matching M of a hypercube, does there exist a Hamiltonian cycle that contains every edge of M? This problem was posed by Ruskey and Savage in 1993, and remains open. If M is a perfect matching a Hamiltonian cycle does exist, as shown by Fink...

Combinatorial Configurations lay between block designs and hypergraphs. When these incidence structures can be embedded in the plane, we call them Geometric Configurations. In this talk, we will explore several results in the study of configurations...

In how many ways can an m x n chessboard be tiled using 2 x 1 tiles? The solution is given by the number of perfect matchings in a related graph. Although computationally difficult in general, in this circumstance we are able to efficiently count...