Date of Award
1-1-2011
Document Type
Dissertation
Degree Name
Ph.D.
Organizational Unit
Mathematics
First Advisor
Petr Vojtechovsky, Ph.D.
Second Advisor
Michael Kinyon
Third Advisor
Rick Ball
Fourth Advisor
Scott Leutenegger
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.
Publication Statement
Copyright is held by the author. User is responsible for all copyright compliance.
Rights Holder
Jon Kyle Pula
Provenance
Received from ProQuest
File Format
application/pdf
Language
en
File Size
93 p.
Recommended Citation
Pula, Jon Kyle, "Approximate Transversals of Latin Squares" (2011). Electronic Theses and Dissertations. 904.
https://digitalcommons.du.edu/etd/904
Copyright date
2011
Discipline
Mathematics