## Transversal This, Transversal That

thesis

posted on 04.04.2019 by DARCY GORDON BEST#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

Latin squares are two-dimensional patterns of symbols. Studied since the 18th century, they now find numerous applications in communication technologies and scheduling problems. A transversal is a balanced selection of symbols within a Latin square. In this thesis, we study the number of, existence of, and structure of transversals in Latin squares and similar objects. In certain sizes of squares, we prove that the number of transversals must be a multiple of four. We also find the first known bound on the number of symbols needed to guarantee the existence of a transversal.