When Transversals Collide

Latin squares are two-dimensional patterns of symbols. A transversal is a balanced selection of symbols within a Latin square. As shown by the famous 18th century mathematician Euler, transversals are central to the important notion of orthogonality in Latin squares. Orthogonal Latin squares are important in pure mathematical areas including combinatorics and finite geometry and have numerous applications in communication technologies, experiment design, and tournament scheduling. In this thesis, we study several different ways that transversals can intersect. We also develop an algorithm for finding transversals.