\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{DFR2005}
\citation{BDLPP1999}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\citation{DFR2005}
\citation{OEIS}
\@writefile{toc}{\contentsline {section}{\numberline {2}The ECO method}{2}{section.2}}
\newlabel{section:definitions}{{2}{2}{The ECO method}{section.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Parametric production matrices and weighted succession rules}{3}{subsection.2.1}}
\citation{DFR2005}
\citation{DFR2005}
\citation{DFR2005}
\citation{DFR2005}
\citation{DFR2005}
\newlabel{fact:seq}{{1}{4}{Fact (iii), \cite {DFR2005}}{theorem.2.1}{}}
\newlabel{fact:gf}{{2}{4}{Fact (v), \cite {DFR2005}}{theorem.2.2}{}}
\newlabel{theorem:gf}{{3}{4}{Theorem 3.2, \cite {DFR2005}}{theorem.2.3}{}}
\newlabel{corollary:recursion}{{4}{4}{Corollary 3.1, \cite {DFR2005}}{theorem.2.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}The Main Example}{4}{section.3}}
\newlabel{section:main}{{3}{4}{The Main Example}{section.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Dyck paths}{4}{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 $y_{1}^{1}y_{3}^{3}$.}}{5}{figure.1}}
\newlabel{fig:path}{{1}{5}{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 $y_{1}^{1}y_{3}^{3}$}{figure.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The matrix}{5}{subsection.3.2}}
\newlabel{theorem:main}{{5}{6}{}{theorem.3.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The generating tree associated with the succession rule of Theorem \ref  {theorem:main}.}}{6}{figure.2}}
\newlabel{fig:gen tree 1}{{2}{6}{The generating tree associated with the succession rule of Theorem \ref {theorem:main}}{figure.2}{}}
\newlabel{cor:f0}{{6}{7}{}{theorem.3.6}{}}
\newlabel{cor:f1}{{7}{7}{}{theorem.3.7}{}}
\newlabel{theorem:equi}{{8}{7}{}{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}.}}{8}{figure.3}}
\newlabel{fig:gen tree 2}{{3}{8}{The generating tree associated with the succession rule of Theorem \ref {theorem:equi}}{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}.}}{9}{figure.4}}
\newlabel{fig:concat}{{4}{9}{Example of the use of the concatenation rule used in the proof of Theorem \ref {theorem:equi}}{figure.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Examples}{9}{subsection.3.3}}
\newlabel{section:spec}{{3.3}{9}{Examples}{subsection.3.3}{}}
\citation{DFR2005}
\bibstyle{plain}
\bibcite{BDLPP1999}{1}
\bibcite{DFR2005}{2}
\bibcite{mans2002}{3}
\bibcite{OEIS}{4}