\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Counting Interesting Semiorders}{1}{section.1}}
\citation{Slo}
\citation{Ber}
\citation{Han}
\citation{Chen}
\newlabel{countbij}{{1}{2}{}{thm.1}{}}
\citation{Pi}
\citation{Pi}
\@writefile{toc}{\contentsline {section}{\numberline {2}Semiorder/Motzkin Path Bijection}{3}{section.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Definitions and Terminology}{3}{subsection.2.1}}
\citation{Pi}
\citation{Pi2}
\newlabel{Def:pttype}{{5}{4}{}{defn.5}{}}
\citation{daveypriestley}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Construction of the Bijection}{5}{subsection.2.2}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The nine possible types of points in a Riordan path.}}{6}{figure.1}}
\newlabel{Fig:pttype}{{1}{6}{The nine possible types of points in a Riordan path}{figure.1}{}}
\citation{Pi}
\newlabel{Thm:bijection}{{2}{7}{}{thm.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces An example of an interesting semiorder $I$, given in matrix and interval representations, and its corresponding path.}}{8}{figure.2}}
\newlabel{Fig:motzkin_example}{{2}{8}{An example of an interesting semiorder $I$, given in matrix and interval representations, and its corresponding path}{figure.2}{}}
\newlabel{Thm:split}{{4}{9}{}{thm.4}{}}
\newlabel{splitmatrix}{{2.2}{10}{Construction of the Bijection}{thm.4}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Constructing the Preimage of $M_m+M_n$}}{10}{figure.3}}
\newlabel{Thm:mirror}{{5}{10}{}{thm.5}{}}
\newlabel{Thm:horiz}{{6}{11}{}{thm.6}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Constructing the Incidence Matrix $ A^h_j$ from $ A$ with $j=6$}}{13}{figure.4}}
\newlabel{Fig:horiz_hp_incidence}{{4}{13}{Constructing the Incidence Matrix $ A^h_j$ from $ A$ with $j=6$}{figure.4}{}}
\newlabel{Lem:height}{{2.2}{14}{}{figure.4}{}}
\newlabel{Thm:upsteps}{{7}{15}{}{thm.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces An example of a Motzkin path $M$.}}{16}{figure.5}}
\newlabel{Fig:horiz_start}{{5}{16}{An example of a Motzkin path $M$}{figure.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces The Motzkin path $M^h_5$}}{16}{figure.6}}
\newlabel{Fig:horiz_finish}{{6}{16}{The Motzkin path $M^h_5$}{figure.6}{}}
\bibcite{daveypriestley}{1}
\bibcite{Ber}{2}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces The Riordan path of base case $n=3$, as well as its interval representation.}}{17}{figure.7}}
\newlabel{Fig:basecase}{{7}{17}{The Riordan path of base case $n=3$, as well as its interval representation}{figure.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Acknowledgement}{17}{section.3}}
\bibcite{Han}{3}
\bibcite{Chen}{4}
\bibcite{Slo}{5}
\bibcite{Pi}{6}
\bibcite{Pi2}{7}
\bibcite{Donaghey}{8}