Approximate Transversals of Latin Squares

<p>A latin square of order <em>n</em> is an <em>n</em> by <em>n</em> array whose entries are drawn from an <em>n</em>-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.</p> <p>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.</p> <p>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.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Year dc:date.available

2011

Author dc:creator

• Pula, Jon Kyle

Contributors dc:contributor

• Petr Vojtechovsky, Ph.D.
• Michael Kinyon
• Rick Ball
• Scott Leutenegger

• Latin square
• Orthogonal mate
• Transversal
• Mathematics

Statement dc:rights

• <p>Copyright is held by the author. User is responsible for all copyright compliance.</p>

Language dc:language

en

Repository record dc:identifier

https://digitalcommons.du.edu/etd/904

OAI identifier oai:identifier

oai:digitalcommons.du.edu:etd-1903