\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]{}
\citation{MacMahonCA}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\citation{MacMahonCA}
\citation{MacMahonMaj}
\citation{RodriguesInv}
\citation{Rearrangements}
\newlabel{ex:first example}{{1}{2}{}{theorem.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Main results}{3}{section.2}}
\citation{SackUlfarsson}
\newlabel{thm:main bijection}{{5}{4}{}{theorem.5}{}}
\newlabel{tab:difference data}{{2}{6}{Main results}{theorem.9}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces The polynomials $G_{n,k}(q)$ for $n=6,8,9$ and $1 \leq k \leq n$.}}{6}{table.1}}
\citation{KnuthVol1}
\citation{MacMahonCA}
\citation{DokosEtAl}
\@writefile{toc}{\contentsline {section}{\numberline {3}Pattern avoidance}{7}{section.3}}
\newlabel{sec:avoidance}{{3}{7}{Pattern avoidance}{section.3}{}}
\newlabel{prop:comp reverse rotate}{{12}{8}{}{theorem.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Avoiding singletons}{8}{subsection.3.1}}
\citation{ErdosSzekeres}
\citation{SimionSchmidt}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Avoiding doubletons}{10}{subsection.3.2}}
\newlabel{prop: 123 132}{{16}{10}{}{theorem.16}{}}
\newlabel{prop: 132 231}{{18}{12}{}{theorem.18}{}}
\bibcite{DokosEtAl}{1}
\bibcite{ErdosSzekeres}{2}
\newlabel{prop: 132 312}{{20}{13}{}{theorem.20}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Acknowledgments}{13}{section.4}}
\bibcite{KnuthVol1}{3}
\bibcite{Rearrangements}{4}
\bibcite{MacMahonMaj}{5}
\bibcite{MacMahonCA}{6}
\bibcite{RodriguesInv}{7}
\bibcite{SackUlfarsson}{8}
\bibcite{SimionSchmidt}{9}
