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Thesis
INVESTIGATING THE ALON-TARSI CONJECTURE USING GRAPH POLYNOMIALS
University of West Florida
Master of Science (MS), University of West Florida
2015
Abstract
A number of works have been published trying to prove the Alon-Tarsi conjecture, and different methods have been used to try to determine the total number of latin squares, as well as the number of even and odd latin squares, of order n. In this thesis we develop a new method for attacking these problems. In Chapter One we discuss the history of latin squares and graph polynomials along with definitions and examples for reference. We also discuss a number of theorems and conjectures in this field of research. Of particular interest are the results given by Douglas S. Stones, and the Huang-White conjecture, which gives very solid connections to the Alon-Tarsi conjecture. In Chapter Two we discuss some of the results from the paper, Combinatorial Nullstellensatz, by Noga Alon. The motivation for using graph polynomials to determine the number of latin squares of order n comes from this paper. The third and fourth chapters contain results about graph polynomials and latin squares. Here we use the graph polynomial of the Rook graph to find the exact number of latin squares of order n.
Details
- Title
- INVESTIGATING THE ALON-TARSI CONJECTURE USING GRAPH POLYNOMIALS
- Resource Type
- Thesis
- Publisher
- University of West Florida
- Format
- text
- Copyright
- http://rightsstatements.org/vocab/InC-EDU/1.0/
- Identifiers
- 99380090863706600
- Academic Unit
- Mathematics and Statistics
- Language
- English
- Awarding Institution
- University of West Florida; Master of Science (MS)
- Theses and Dissertations
- Master of Science (MS), University of West Florida