Darcy Best

A set of unit vectors $V \subset \mathbb{C}^n$ is called {\it biangular} if for any $u,v \in V, u \neq v$, $$|\langle u,v\rangle| \in \left\{0,\alpha\right\}$$ for some $0 \alpha 1$. There are well-known upper bounds on the size of these sets of...

A transversal of a latin square of order n is a subset of entries picked in such a way that each row, each column and each symbol is present at most once. In many latin squares, you can find a full transversal by selecting n entries which do not...

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...

We will discuss several results related to transversals in Latin squares (think "Sudoku") and other Latin square-like objects. These results centre around showing the existence of, the number of, or the structure of transversals in different cases...