\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{Ard}
\citation{Ath}
\citation{PoSt}
\citation{Seo}
\citation{Sta3}
\citation{Sta3}
\citation{Seo}
\citation{Ath}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\citation{Comt}
\citation{OT}
\citation{Sta3}
\citation{Za}
\@writefile{toc}{\contentsline {section}{\numberline {2}Preliminaries}{2}{section.2}}
\newlabel{sec2}{{2}{2}{Preliminaries}{section.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Basic concepts of hyperplane arrangements}{2}{subsection.2.1}}
\newlabel{eq:Zas}{{2}{2}{Zaslavsky \cite {Za}}{theorem.2}{}}
\citation{Ath}
\citation{CH}
\citation{Sta3}
\citation{Comt}
\newlabel{eq:cat-c}{{2.1}{3}{Basic concepts of hyperplane arrangements}{theorem.3}{}}
\newlabel{eq:cat-r}{{2.1}{3}{Basic concepts of hyperplane arrangements}{theorem.3}{}}
\newlabel{eqn:thr-c}{{2.1}{3}{Basic concepts of hyperplane arrangements}{theorem.3}{}}
\citation{Sul}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Delannoy numbers and Schr\"oder numbers}{4}{subsection.2.2}}
\newlabel{id_Del1}{{1}{4}{}{equation.2.1}{}}
\newlabel{id_Del2}{{2}{4}{}{equation.2.2}{}}
\newlabel{rec_Del}{{3}{4}{}{equation.2.3}{}}
\newlabel{gf_cDel}{{4}{4}{}{equation.2.4}{}}
\newlabel{gf_Sch}{{5}{4}{}{equation.2.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Graph $G_{11}$}}{5}{figure.1}}
\newlabel{fig:Gq}{{1}{5}{Graph $G_{11}$}{figure.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Main result}{5}{section.3}}
\newlabel{sec3}{{3}{5}{Main result}{section.3}{}}
\newlabel{def:catarr}{{6}{5}{Main result}{equation.3.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}The characteristic polynomial of ${\mathcal  {CT}}_n$}{5}{subsection.3.1}}
\newlabel{eq:setX}{{7}{5}{The characteristic polynomial of $\CT _n$}{equation.3.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Graphs $A_3$ and $B_3$}}{6}{figure.2}}
\newlabel{fig:AB}{{2}{6}{Graphs $A_3$ and $B_3$}{figure.2}{}}
\newlabel{lem:abD}{{6}{6}{}{theorem.6}{}}
\newlabel{id_b-Del}{{8}{6}{}{equation.3.8}{}}
\newlabel{id_a-Del}{{9}{6}{}{equation.3.9}{}}
\newlabel{rec_b}{{3.1}{6}{The characteristic polynomial of $\CT _n$}{equation.3.9}{}}
\newlabel{lem:select}{{7}{7}{}{theorem.7}{}}
\newlabel{eq:select-a}{{7}{7}{}{theorem.7}{}}
\newlabel{eq:select-b}{{7}{7}{}{theorem.7}{}}
\newlabel{eq:amn}{{10}{7}{The characteristic polynomial of $\CT _n$}{equation.3.10}{}}
\newlabel{eq:bmn}{{11}{7}{The characteristic polynomial of $\CT _n$}{equation.3.11}{}}
\newlabel{thm:ch-poly}{{8}{8}{Main result}{theorem.8}{}}
\newlabel{eq:main}{{12}{8}{Main result}{equation.3.12}{}}
\newlabel{lin-combin}{{13}{8}{The characteristic polynomial of $\CT _n$}{equation.3.13}{}}
\citation{Slo1}
\citation{Wi}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The exponential generating function for $\chi _{{\mathcal  {CT}}_n}(t)$}{9}{subsection.3.2}}
\newlabel{eq:gen-amn-m}{{14}{9}{The exponential generating function for $\cpct (t)$}{equation.3.14}{}}
\newlabel{eq:gen-amn-l}{{15}{9}{The exponential generating function for $\cpct (t)$}{equation.3.15}{}}
\newlabel{eq:gen-amn-r}{{16}{10}{The exponential generating function for $\cpct (t)$}{equation.3.16}{}}
\newlabel{eq:gen-amn}{{3.2}{10}{The exponential generating function for $\cpct (t)$}{equation.3.16}{}}
\newlabel{eq:gen-amn1}{{3.2}{10}{The exponential generating function for $\cpct (t)$}{equation.3.16}{}}
\bibcite{Ard}{1}
\bibcite{Ath}{2}
\bibcite{CH}{3}
\bibcite{Comt}{4}
\bibcite{OT}{5}
\bibcite{PoSt}{6}
\newlabel{eq:gen-cha-ct}{{17}{11}{The exponential generating function for $\cpct (t)$}{equation.3.17}{}}
\newlabel{eq:gen-reg-ct}{{18}{11}{The exponential generating function for $\cpct (t)$}{equation.3.18}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Remark}{11}{subsection.3.3}}
\newlabel{arr:gen}{{3.3}{11}{Remark}{subsection.3.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Acknowledgments}{11}{section.4}}
\bibcite{Seo}{7}
\bibcite{Slo1}{8}
\bibcite{Sta3}{9}
\bibcite{Sul}{10}
\bibcite{Wi}{11}
\bibcite{Za}{12}
