UWF-Thesis.tex

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% Enables embedding sage in LaTex
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% Define commands for document variables
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%----------------------------------------------------------------------------------------
%	DOCUMENT VARIABLES
%	Fill in the lines below to update the thesis template
%	If you wish to cite each of the variables defined below, look at the
%	section above for the citation command e.g. \examiner{} below is
%	defined as \examname above so you cite it as \examname
%----------------------------------------------------------------------------------------

\thesistitle{INVESTIGATING THE ALON-TARSI CONJECTURE \\USING GRAPH POLYNOMIALS} % Your thesis title - this is used in the title and abstract
%-------------------------------------------------
\supervisor{Jaromy S. Kuhl, Ph.D.} % You supervisor's name - this is used in the signature page
%-------------------------------------------------
\deptchair{Jaromy S. Kuhl, Ph.D.} % You department chair's name - this is used in the signature page
%-------------------------------------------------
\dean{Richard S. Podemski, Ph.D.} % You dean's name - this is used in the signature page
%-------------------------------------------------
\committeememberone{Avinash Dalal, Ph.D.} % Your committee memeber's name - this is used in the signature page
%-------------------------------------------------
\committeemembertwo{Morris L. Marx, Ph.D.} % Your committee memeber's name - this is used in the signature page
%-------------------------------------------------
\committeememberthree{Rohan Hemasinha, Ph.D.} % Your committee memeber's name - this is used in the signature page
%-------------------------------------------------
\degree{Master of Science} % Your degree name - this is currently used in the title page
%-------------------------------------------------
\undergraddegree{B.S., University of Central Florida, 2006} % Your undergrad degree name - this is currently used in the title page
%-------------------------------------------------
\graddegree{} % Your graduate degree name - this is currently used in the title page (for dissertation only)
%-------------------------------------------------
\authors{Wayne Joseph Jacobson} % Your name - this is used in the title page, signature page, and abstract
%-------------------------------------------------
\addresses{} % Your address - this is not currently used anywhere in the template, cite it with \addressnames if you want it
%-------------------------------------------------
\subject{} % Your subject area - this is not currently used anywhere in the template, cite it with \subjectname if you want it
%-------------------------------------------------
\keywords{} % Keywords for your thesis - this is not currently used anywhere in the template, cite it with \keywordnames if you want it
%-------------------------------------------------
\university{\texorpdfstring{\href{http://www.uwf.edu} % Your university's URL
                {The University of West Florida}} % Your university's name - this is currently used in the title page
                {The University of West Florida}}
%-------------------------------------------------
\department{\texorpdfstring{\href{http://uwf.edu/cse/departments/mathematics-and-statistics/} % Your department's URL
                {Department of Mathematics and Statistics}} % Your department's name - used in the title page 
                {Department of Mathematics and Statistics}}
%-------------------------------------------------
\group{\texorpdfstring{\href{http://uwf.edu/cse/} % Your research group's URL
                {College of Science, Engineering, and Health}} % Your research group's name - this is currently used in the title page
                {College of Science, Engineering, and Health}}
%-------------------------------------------------

\begin{document}

\pagenumbering{roman} % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages
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%	TITLE PAGE
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\begin{titlepage}
\begin{center}
\ttitle

\vspace*{\fill}
by\\
\authornames \\
\ugdegreename \\
\vspace*{\fill}

\setstretch{1.0} % Line spacing
A thesis submitted to the \deptname \\
\groupname \\
\univname \\
In partial fulfillment of the requirements for the degree of\\
\degreename

\setstretch{1.65} % Line spacing
{\the\year} \\ % Date

\end{center}
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%	COPYRIGHT PAGE
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\copyright \authornames
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%	SIGNATURE PAGE
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\pagestyle{empty} % No headers or footers for the following pages
The thesis of \authornames\xspace is approved:
\begin{center}
\begin{tabular}{ll}
\multicolumn{2}{c}{} \\
\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
\comnameA, Committee Member & Date\\
&\\
\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
\comnameB, Ph.D., Committee Member & Date\\
&\\
\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
\supname, Committee Chair & Date\\
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\vspace{3cm}
Accepted for the Department/Division:
\begin{center}
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\multicolumn{2}{c}{} \\
\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
\chairname, Chair & Date 
\end{tabular}
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\vspace{2cm}
Accepted for the University:
\begin{center}
\begin{tabular}{ll}
\multicolumn{2}{c}{} \\
\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
\deanname, Dean, Graduate School & Date
\end{tabular}
\end{center}
\clearpage % Start a new page

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%	ACKNOWLEDGMENTS
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\addtotoc{ACKNOWLEDGMENTS} % Add the "Acknowledgments" page entry to the Contents
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\begin{center}{ACKNOWLEDGMENTS}\end{center}
\tab I would like to thank The University of West Florida for giving me the opportunity to continue my
education. I would also like to thank the Department of Mathematics and Statistics in particular for
the rigor and level of the program that I have enjoyed over the past two years.\\
\tab I would also like to thank my family and friends for their help and support in my adventure. I would like to thank
my mother for her positive attitude and support, my father for all of his help during my studies and
tutoring sessions, and my wife for everything over the last two years.
\clearpage % Start a new page

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%	LIST OF CONTENTS/FIGURES/TABLES PAGES
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\tableofcontents
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\listoffigures % Write out the List of Figures
\addtotoc{LIST OF FIGURES} % Add the "LOF" page entry to the Contents
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%	ABSTRACT PAGE
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\addtotoc{ABSTRACT} % Add the "Abstract" page entry to the Contents

\begin{center}
ABSTRACT\\
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\ttitle
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\\
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\authornames
\end{center}
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\tab 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.\\
\tab 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.\\
\tab In Chapter Two we discuss some of the results from the paper, \textit{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.\\
\tab 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 $n$.
\clearpage % Start a new page

\pagenumbering{arabic}
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%	THESIS CONTENT - CHAPTERS
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\pagestyle{fancy}
\input{./Chapters/Chapter1}
\input{./Chapters/Chapter2}

%----------------------------------------------------------------------------------------
%	BIBLIOGRAPHY
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%\pagestyle{plain}
\bibliographystyle{unsrtnat} % Use the "unsrtnat" BibTeX style for formatting the Bibliography
\bibliography{Bibliography} % The references information are stored in the file "Bibliography.bib"
\addtotoc{REFERENCES}

%----------------------------------------------------------------------------------------
%	THESIS CONTENT - APPENDICES
%----------------------------------------------------------------------------------------
\pagestyle{plain}
\addtotoc{APPENDIXES}
\appendix % Cue to tell LaTeX that the following 'chapters' are Appendices
\input{./Appendices/AppendixA}

\end{document}