\relax 
\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{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\citation{Brylawski}
\citation{Stanley1}
\citation{GuilbaudRosenstiehl}
\citation{Tamari}
\citation{EdelmanSimion}
\citation{SimionUllman}
\citation{Sloane}
\citation{Sloane}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{section1}{{1}{1}{Introduction\relax }{section.1}{}}
\citation{PS}
\@writefile{toc}{\contentsline {section}{\numberline {2}Preliminaries}{2}{section.2}}
\newlabel{section2}{{2}{2}{Preliminaries\relax }{section.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A Dyck path and its corresponding word}}{2}{figure.1}}
\newlabel{fig1}{{1}{2}{Preliminaries\relax }{figure.1}{}}
\citation{NarayanaFulton}
\citation{Pergola}
\citation{Kreweras2}
\citation{Kreweras1}
\citation{FerrariPinzani}
\citation{Stanley1}
\citation{Deutsch}
\@writefile{toc}{\contentsline {section}{\numberline {3}Chains and Ranks}{3}{section.3}}
\newlabel{section3}{{3}{3}{Chains and Ranks\relax }{section.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The Hasse diagram of $\@mathcal {D}_4$}}{4}{figure.2}}
\newlabel{fig2}{{2}{4}{Preliminaries\relax }{figure.2}{}}
\newlabel{prop1}{{3.1}{4}{Chains and Ranks\relax }{tm.3.1}{}}
\citation{FerrariPinzani}
\citation{FerrariPinzani}
\newlabel{eq0}{{1}{5}{Chains and Ranks\relax }{equation.1}{}}
\newlabel{relation2}{{2}{5}{Chains and Ranks\relax }{equation.2}{}}
\citation{Deutsch}
\@writefile{toc}{\contentsline {section}{\numberline {4}Fillings and Degrees}{6}{section.4}}
\newlabel{section4}{{4}{6}{Fillings and Degrees\relax }{section.4}{}}
\citation{Deutsch}
\newlabel{eq1}{{3}{7}{Fillings and Degrees\relax }{equation.3}{}}
\newlabel{equation4}{{4}{7}{Fillings and Degrees\relax }{equation.4}{}}
\newlabel{equation5}{{5}{7}{Fillings and Degrees\relax }{equation.5}{}}
\newlabel{equation6}{{6}{7}{Fillings and Degrees\relax }{equation.6}{}}
\citation{Sloane}
\newlabel{prop4.5}{{4.4}{8}{Fillings and Degrees\relax }{tm.4.4}{}}
\citation{Stanley1}
\citation{BarnabeiPezzoli}
\@writefile{toc}{\contentsline {section}{\numberline {5}The M\"obius function}{10}{section.5}}
\newlabel{section5}{{5}{10}{The M\"obius function\relax }{section.5}{}}
\newlabel{prop5.1}{{5.1}{10}{The M\"obius function\relax }{tm.5.1}{}}
\newlabel{lemma5.2}{{5.2}{10}{The M\"obius function\relax }{tm.5.2}{}}
\citation{Edelman}
\citation{Sloane}
\newlabel{eq2}{{7}{12}{The M\"obius function\relax }{equation.7}{}}
\citation{EdelmanGreene}
\citation{Stanley3}
\@writefile{toc}{\contentsline {section}{\numberline {6}Dyck paths and permutations}{13}{section.6}}
\newlabel{section6}{{6}{13}{Dyck paths and permutations\relax }{section.6}{}}
\newlabel{prop6.1}{{6.1}{13}{Dyck paths and permutations\relax }{tm.6.1}{}}
\citation{BK}
\citation{BBFP}
\citation{Fulmek}
\newlabel{prop6.2}{{6.2}{14}{Dyck paths and permutations\relax }{tm.6.2}{}}
\newlabel{lemma6.3}{{6.3}{14}{Dyck paths and permutations\relax }{tm.6.3}{}}
\newlabel{eq3}{{8}{14}{Dyck paths and permutations\relax }{equation.8}{}}
\newlabel{eq4}{{9}{15}{Dyck paths and permutations\relax }{equation.9}{}}
\bibcite{BK}{1}
\bibcite{BBFP}{2}
\bibcite{BarnabeiPezzoli}{3}
\bibcite{Brylawski}{4}
\bibcite{Deutsch}{5}
\bibcite{Edelman}{6}
\bibcite{EdelmanGreene}{7}
\bibcite{EdelmanSimion}{8}
\bibcite{FerrariPinzani}{9}
\bibcite{Fulmek}{10}
\bibcite{GuilbaudRosenstiehl}{11}
\bibcite{NarayanaFulton}{12}
\bibcite{Kreweras2}{13}
\bibcite{Kreweras1}{14}
\bibcite{PS}{15}
\bibcite{Pergola}{16}
\bibcite{SimionUllman}{17}
\bibcite{Sloane}{18}
\bibcite{Stanley3}{19}
\bibcite{Stanley1}{20}
\bibcite{Tamari}{21}