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Transversal This, Transversal That

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thesis
posted on 04.04.2019 by DARCY GORDON BEST
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.

History

Campus location

Australia

Principal supervisor

Ian Murray Wanless

Additional supervisor 1

Heiko Dietrich

Additional supervisor 2

Daniel Horsley

Year of Award

2018

Department, School or Centre

Mathematical Sciences

Course

Doctor of Philosophy

Degree Type

DOCTORATE

Faculty

Faculty of Science

Exports