\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{DFR2005}
\citation{BDLPP1999}
\citation{DFR2005}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{3}{section.1}}
\citation{OEIS}
\@writefile{toc}{\contentsline {section}{\numberline {2}The ECO method}{4}{section.2}}
\newlabel{section:definitions}{{2}{4}{The ECO method\relax }{section.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Parametric production matrices and weighted succession rules}{5}{subsection.2.1}}
\citation{DFR2005}
\citation{DFR2005}
\citation{DFR2005}
\citation{DFR2005}
\citation{DFR2005}
\newlabel{fact:seq}{{1}{6}{Parametric production matrices and weighted succession rules\relax }{theorem.2.1}{}}
\newlabel{fact:gf}{{2}{6}{Parametric production matrices and weighted succession rules\relax }{theorem.2.2}{}}
\newlabel{theorem:gf}{{3}{6}{Parametric production matrices and weighted succession rules\relax }{theorem.2.3}{}}
\newlabel{corollary:recursion}{{4}{6}{Parametric production matrices and weighted succession rules\relax }{theorem.2.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}The Main Example}{6}{section.3}}
\newlabel{section:main}{{3}{6}{The Main Example\relax }{section.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Dyck paths}{6}{subsection.3.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A Dyck path of semilength 9. The height of the rises are, in order, 1,2,0,1,0. The path has 4 high peaks, of heights 1,3,3,3. Using succession rule $\Omega $ of Theorem \ref  {theorem:main} the path will have weight $x_{0}^{5}x_{1}x_{2}^{3}y_{1}^{1}y_{2}^{2}y_{4}^{1}$. Using succession rule $\Omega ^{\prime }$ of Theorem \ref  {theorem:equi} the path will have weight $y_{1}^{1}y_{3}^{3}$.}}{7}{figure.1}}
\newlabel{fig:path}{{1}{7}{Dyck paths\relax }{figure.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The matrix}{7}{subsection.3.2}}
\newlabel{theorem:main}{{5}{7}{The matrix\relax }{theorem.3.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The generating tree associated with the succession rule of Theorem \ref  {theorem:main}.}}{8}{figure.2}}
\newlabel{fig:gen tree 1}{{2}{8}{The matrix\relax }{figure.2}{}}
\newlabel{cor:f0}{{6}{9}{The matrix\relax }{theorem.3.6}{}}
\newlabel{cor:f1}{{7}{9}{The matrix\relax }{theorem.3.7}{}}
\newlabel{theorem:equi}{{8}{9}{The matrix\relax }{theorem.3.8}{}}
\citation{mans2002}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The generating tree associated with the succession rule of Theorem \ref  {theorem:equi}.}}{10}{figure.3}}
\newlabel{fig:gen tree 2}{{3}{10}{The matrix\relax }{figure.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Example of the use of the concatenation rule used in the proof of Theorem \ref  {theorem:equi}.}}{10}{figure.4}}
\newlabel{fig:concat}{{4}{10}{The matrix\relax }{figure.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Examples}{11}{subsection.3.3}}
\newlabel{section:spec}{{3.3}{11}{Examples\relax }{subsection.3.3}{}}
\citation{DFR2005}
\bibstyle{abbrv}
\bibcite{BDLPP1999}{1}
\bibcite{DFR2005}{2}
\bibcite{mans2002}{3}
\bibcite{OEIS}{4}