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% Enables Chapters and Sections to be centered
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\usepackage[square, numbers, comma, sort&compress]{natbib} % Use the natbib reference package - read up on this to edit the reference style; if you want text (e.g. Smith et al., 2012) for the in-text references (instead of numbers), remove 'numbers'
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\renewcommand{\bibname}{REFERENCES}
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\usepackage{xspace}
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% Enables embedding sage in LaTex
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\usepackage{sagetex}
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% Define commands for document variables
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\newcommand*{\supervisor}[1]{\def\supname{#1}}
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%----------------------------------------------------------------------------------------
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%	DOCUMENT VARIABLES
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%	Fill in the lines below to update the thesis template
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%	If you wish to cite each of the variables defined below, look at the
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%	section above for the citation command e.g. \examiner{} below is
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%	defined as \examname above so you cite it as \examname
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%----------------------------------------------------------------------------------------
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\thesistitle{INVESTIGATING THE ALON-TARSI CONJECTURE \\USING GRAPH POLYNOMIALS} % Your thesis title - this is used in the title and abstract
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%-------------------------------------------------
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\supervisor{Jaromy S. Kuhl, Ph.D.} % You supervisor's name - this is used in the signature page
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%-------------------------------------------------
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\deptchair{Jaromy S. Kuhl, Ph.D.} % You department chair's name - this is used in the signature page
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%-------------------------------------------------
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\dean{Richard S. Podemski, Ph.D.} % You dean's name - this is used in the signature page
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%-------------------------------------------------
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\committeememberone{Avinash Dalal, Ph.D.} % Your committee memeber's name - this is used in the signature page
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%-------------------------------------------------
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\committeemembertwo{Morris L. Marx, Ph.D.} % Your committee memeber's name - this is used in the signature page
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%-------------------------------------------------
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\committeememberthree{Rohan Hemasinha, Ph.D.} % Your committee memeber's name - this is used in the signature page
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%-------------------------------------------------
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\degree{Master of Science} % Your degree name - this is currently used in the title page
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%-------------------------------------------------
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\undergraddegree{B.S., University of Central Florida, 2006} % Your undergrad degree name - this is currently used in the title page
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%-------------------------------------------------
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\graddegree{} % Your graduate degree name - this is currently used in the title page (for dissertation only)
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%-------------------------------------------------
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\authors{Wayne Joseph Jacobson} % Your name - this is used in the title page, signature page, and abstract
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%-------------------------------------------------
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\addresses{} % Your address - this is not currently used anywhere in the template, cite it with \addressnames if you want it
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%-------------------------------------------------
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\subject{} % Your subject area - this is not currently used anywhere in the template, cite it with \subjectname if you want it
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%-------------------------------------------------
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\keywords{} % Keywords for your thesis - this is not currently used anywhere in the template, cite it with \keywordnames if you want it
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%-------------------------------------------------
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\university{\texorpdfstring{\href{http://www.uwf.edu} % Your university's URL
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                {The University of West Florida}} % Your university's name - this is currently used in the title page
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                {The University of West Florida}}
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%-------------------------------------------------
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\department{\texorpdfstring{\href{http://uwf.edu/cse/departments/mathematics-and-statistics/} % Your department's URL
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                {Department of Mathematics and Statistics}} % Your department's name - used in the title page 
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                {Department of Mathematics and Statistics}}
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%-------------------------------------------------
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\group{\texorpdfstring{\href{http://uwf.edu/cse/} % Your research group's URL
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                {College of Science, Engineering, and Health}} % Your research group's name - this is currently used in the title page
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                {College of Science, Engineering, and Health}}
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%-------------------------------------------------
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\begin{document}
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\pagenumbering{roman} % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages
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%----------------------------------------------------------------------------------------
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%	TITLE PAGE
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%----------------------------------------------------------------------------------------
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\pagestyle{empty} % No headers or footers for the following pages
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\setstretch{1.65} % Line spacing
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\begin{titlepage}
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\begin{center}
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\ttitle
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\vspace*{\fill}
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by\\
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\authornames \\
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\ugdegreename \\
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\vspace*{\fill}
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\setstretch{1.0} % Line spacing
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A thesis submitted to the \deptname \\
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\groupname \\
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\univname \\
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In partial fulfillment of the requirements for the degree of\\
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\degreename
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\setstretch{1.65} % Line spacing
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{\the\year} \\ % Date
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\end{center}
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\end{titlepage}
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%----------------------------------------------------------------------------------------
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%	COPYRIGHT PAGE
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%----------------------------------------------------------------------------------------
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\pagestyle{empty} % No headers or footers for the following pages
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\vspace*{\fill}
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\begin{center}
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\copyright \authornames
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\end{center}
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\vspace*{\fill}
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\clearpage % Start a new page
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%----------------------------------------------------------------------------------------
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%	SIGNATURE PAGE
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%----------------------------------------------------------------------------------------
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\pagestyle{empty} % No headers or footers for the following pages
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The thesis of \authornames\xspace is approved:
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\begin{center}
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\begin{tabular}{ll}
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\multicolumn{2}{c}{} \\
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\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
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\comnameA, Committee Member & Date\\
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&\\
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\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
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\comnameB, Ph.D., Committee Member & Date\\
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&\\
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\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
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\supname, Committee Chair & Date\\
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\end{tabular}
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\end{center}
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\vspace{3cm}
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Accepted for the Department/Division:
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\begin{center}
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\begin{tabular}{ll}
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\multicolumn{2}{c}{} \\
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\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
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\chairname, Chair & Date 
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\end{tabular}
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\end{center}
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\vspace{2cm}
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Accepted for the University:
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\begin{center}
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\begin{tabular}{ll}
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\multicolumn{2}{c}{} \\
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\rule{9cm}{1pt} & \rule{4cm}{1pt} \\
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\deanname, Dean, Graduate School & Date
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\end{tabular}
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\end{center}
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\clearpage % Start a new page
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%----------------------------------------------------------------------------------------
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%	ACKNOWLEDGMENTS
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%----------------------------------------------------------------------------------------
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\pagestyle{plain}
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\addtotoc{ACKNOWLEDGMENTS} % Add the "Acknowledgments" page entry to the Contents
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\setstretch{1.65} % Line spacing
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\begin{center}{ACKNOWLEDGMENTS}\end{center}
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\tab I would like to thank The University of West Florida for giving me the opportunity to continue my
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education. I would also like to thank the Department of Mathematics and Statistics in particular for
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the rigor and level of the program that I have enjoyed over the past two years.\\
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\tab I would also like to thank my family and friends for their help and support in my adventure. I would like to thank
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my mother for her positive attitude and support, my father for all of his help during my studies and
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tutoring sessions, and my wife for everything over the last two years.
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\clearpage % Start a new page
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%----------------------------------------------------------------------------------------
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%	LIST OF CONTENTS/FIGURES/TABLES PAGES
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%----------------------------------------------------------------------------------------
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\pagestyle{plain}
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\setstretch{1.0} % Line spacing
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\tableofcontents
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\clearpage
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\listoftables % Write out the List of Tables
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\addtotoc{LIST OF TABLES} % Add the "LOT" page entry to the Contents
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\clearpage % Start a new page
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\listoffigures % Write out the List of Figures
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\addtotoc{LIST OF FIGURES} % Add the "LOF" page entry to the Contents
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\clearpage % Start a new page
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%----------------------------------------------------------------------------------------
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%	ABSTRACT PAGE
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%----------------------------------------------------------------------------------------
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\pagestyle{plain}
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\addtotoc{ABSTRACT} % Add the "Abstract" page entry to the Contents
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\begin{center}
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ABSTRACT\\
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\setstretch{1.65} % Line spacing
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\ttitle
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\setstretch{1.0} % Line spacing
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\\
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\setstretch{1.65} % Line spacing
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\authornames
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\end{center}
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\setstretch{1.65} % Line spacing
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\tab A number of works have been published trying to prove the Alon-Tarsi conjecture, and
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different methods have been used to try to determine the total number of latin squares, as well as
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the number of even and odd latin squares, of order $n$. In this thesis we develop a new method for
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attacking these problems.\\
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\tab In Chapter One we discuss the history of latin squares and graph polynomials along with
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definitions and examples for reference. We also discuss a number of theorems and conjectures in
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this field of research. Of particular interest are the results given by Douglas S. Stones, and the
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Huang-White conjecture, which gives very solid connections to the Alon-Tarsi conjecture.\\
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\tab In Chapter Two we discuss some of the results from the paper, \textit{Combinatorial Nullstellensatz},
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by Noga Alon. The motivation for using graph polynomials to determine the number of latin
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squares of order $n$ comes from this paper.\\
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\tab The third and fourth chapters contain results about graph polynomials and latin squares. Here
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we use the graph polynomial of the Rook graph to find the exact number of latin squares of order $n$.
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\clearpage % Start a new page
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\pagenumbering{arabic}
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%----------------------------------------------------------------------------------------
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%	THESIS CONTENT - CHAPTERS
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%----------------------------------------------------------------------------------------
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\pagestyle{fancy}
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\input{./Chapters/Chapter1}
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\input{./Chapters/Chapter2}
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%----------------------------------------------------------------------------------------
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%	BIBLIOGRAPHY
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%----------------------------------------------------------------------------------------
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%\pagestyle{plain}
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\bibliographystyle{unsrtnat} % Use the "unsrtnat" BibTeX style for formatting the Bibliography
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\bibliography{Bibliography} % The references information are stored in the file "Bibliography.bib"
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\addtotoc{REFERENCES}
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%----------------------------------------------------------------------------------------
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%	THESIS CONTENT - APPENDICES
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%----------------------------------------------------------------------------------------
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\pagestyle{plain}
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\addtotoc{APPENDIXES}
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\appendix % Cue to tell LaTeX that the following 'chapters' are Appendices
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\input{./Appendices/AppendixA}
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\end{document}
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