Lethbridge Number Theory and Combinatorics Seminar: Darcy Best

A transversal of a latin square of order n is a set of n entries picked in such a way that no row, column or symbol is present more than once. As you add more symbols to a latin square, you expect the number of transversals to increase. We show that once the number of symbols reaches a certain threshold, the square is guaranteed to have a transversal.