Date of Award

1-1-2011

Document Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics

First Advisor

Petr Vojtechovsky

Keywords

latin square, orthogonal mate, transversal

Abstract

A latin square of order n is an n by n array whose entries are drawn from an n-set of symbols such that each symbol appears precisely once in each row and column. A transversal of a latin square is a subset of cells that meets each row, column, and symbol precisely once.

There are many open and difficult questions about the existence and prevalence of transversals. We undertake a systematic study of collections of cells that exhibit regularity properties similar to those of transversals and prove numerous theorems about their existence and structure. We hope that our results and methods will suggest new strategies for the study of transversals.

The main topics we investigate are partial and weak transversals, weak orthogonal mates, integral weight functions on the cells of a latin square, applications of Alon's Combinatorial Nullstellensatz to latin squares, and complete mappings of finite loops.

Provenance

Recieved from ProQuest

Rights holder

Jon Kyle Pula

File size

93 p.

File format

application/pdf

Language

en

Discipline

Mathematics

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