10.4225/03/5b164871dee8e
DARCY GORDON BEST
Transversal This, Transversal That
2019
Monash University
Latin Squares
Transversals
Mutually Orthogonal Latin Squares
Permanents
2019-04-04 04:40:13
article
https://monash.figshare.com/articles/Transversal_This_Transversal_That/6444785
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.