\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{EC2}
\citation{catalan}
\citation{dickson}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{e-1}{{1.1}{1}{Introduction\relax }{equation.1.1}{}}
\citation{gessel}
\citation{gessel}
\citation{shapiro}
\citation{gessel}
\citation{gessel}
\newlabel{e-8}{{1.2}{2}{Introduction\relax }{equation.1.2}{}}
\newlabel{e-mo}{{1.3}{2}{Introduction\relax }{equation.1.3}{}}
\newlabel{e-2}{{1.4}{2}{Introduction\relax }{equation.1.4}{}}
\citation{gilles}
\citation{nicholas}
\citation{callan}
\@writefile{toc}{\contentsline {section}{\numberline {2}The main theorem}{3}{section.2}}
\newlabel{s-main}{{2}{3}{The main theorem\relax }{section.2}{}}
\newlabel{l-main}{{2.1}{3}{The main theorem\relax }{thm.2.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces First step of the bijection}}{4}{figure.1}}
\newlabel{f-pic1}{{1}{4}{The main theorem\relax }{figure.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Second step of the bijection}}{4}{figure.2}}
\newlabel{f-pic2}{{2}{4}{The main theorem\relax }{figure.2}{}}
\newlabel{t-main}{{2.2}{4}{The main theorem\relax }{thm.2.2}{}}
\citation{de-Bruijn}
\@writefile{toc}{\contentsline {section}{\numberline {3}An algebraic proof and further results}{5}{section.3}}
\newlabel{l-G}{{3.1}{5}{An algebraic proof and further results\relax }{thm.3.1}{}}
\newlabel{e-G}{{3.1}{5}{An algebraic proof and further results\relax }{equation.3.1}{}}
\newlabel{t-firstsum}{{3.2}{5}{An algebraic proof and further results\relax }{thm.3.2}{}}
\newlabel{e-Psi}{{3}{6}{An algebraic proof and further results\relax }{thm.3.2}{}}
\newlabel{l-general}{{3.3}{7}{An algebraic proof and further results\relax }{thm.3.3}{}}
\newlabel{t-general}{{3.4}{8}{An algebraic proof and further results\relax }{thm.3.4}{}}
\newlabel{e-general}{{3.2}{8}{An algebraic proof and further results\relax }{equation.3.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}A combinatorial interpretation for $T(3,n)$}{8}{section.4}}
\newlabel{e-sqrt}{{4.1}{8}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.1}{}}
\newlabel{l-gf}{{4.1}{9}{A combinatorial interpretation for $T(3,n)$\relax }{thm.4.1}{}}
\newlabel{e-3paths}{{4.3}{9}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.3}{}}
\newlabel{e-ugly3}{{4.4}{9}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.4}{}}
\newlabel{t-Gij}{{4.2}{10}{A combinatorial interpretation for $T(3,n)$\relax }{thm.4.2}{}}
\newlabel{e-Gj}{{4.5}{10}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.5}{}}
\newlabel{e-Gij}{{4.6}{10}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.6}{}}
\citation{sato-cong}
\citation{kratt}
\bibcite{de-Bruijn}{1}
\bibcite{callan}{2}
\bibcite{catalan}{3}
\bibcite{dickson}{4}
\bibcite{gessel}{5}
\bibcite{kratt}{6}
\bibcite{nicholas}{7}
\bibcite{sato-cong}{8}
\bibcite{gilles}{9}
\bibcite{shapiro}{10}
\newlabel{t-T3}{{4.3}{12}{A combinatorial interpretation for $T(3,n)$\relax }{thm.4.3}{}}
\newlabel{e-T3}{{4.7}{12}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.7}{}}
\newlabel{e-5/2}{{4.8}{12}{A combinatorial interpretation for $T(3,n)$\relax }{equation.4.8}{}}
\bibcite{EC2}{11}