\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]{}
\HyPL@Entry{0<</S/D>>}
\citation{harpe}
\citation{Ca1}
\citation{Ca2}
\citation{Floyd}
\citation{bartholdi}
\citation{BFP}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\citation{Brandani2006}
\citation{Albuquerque2009a}
\citation{Ungerboeck1987}
\citation{Be}
\@writefile{toc}{\contentsline {section}{\numberline {2}Growth of hyperbolic tessellations}{3}{section.2}}
\citation{Sullivan}
\newlabel{equiv}{{1}{4}{Growth of hyperbolic tessellations}{equation.2.1}{}}
\newlabel{eq2}{{2}{5}{Growth of hyperbolic tessellations}{equation.2.2}{}}
\newlabel{prop1}{{1}{7}{}{theorem.1}{}}
\newlabel{prop2}{{2}{7}{}{theorem.2}{}}
\newlabel{iota}{{3}{8}{Growth of hyperbolic tessellations}{equation.2.3}{}}
\newlabel{prop3}{{3}{8}{}{theorem.3}{}}
\newlabel{418}{{4}{8}{}{theorem.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Recursive counting functions for the growth of the group $\Gamma _{p,q}$}{9}{section.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Counting the polygons}{9}{subsection.3.1}}
\newlabel{eq4}{{4}{9}{Counting the polygons}{equation.3.4}{}}
\newlabel{eq5}{{5}{10}{Counting the polygons}{equation.3.5}{}}
\newlabel{eq6}{{6}{10}{Counting the polygons}{equation.3.6}{}}
\newlabel{eq7}{{7}{10}{Counting the polygons}{equation.3.7}{}}
\newlabel{eq8}{{8}{10}{Counting the polygons}{equation.3.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Counting the vertices}{10}{subsection.3.2}}
\newlabel{eq10}{{10}{11}{Counting the vertices}{equation.3.10}{}}
\newlabel{eq11}{{11}{11}{Counting the vertices}{equation.3.11}{}}
\newlabel{eq12}{{12}{11}{Counting the vertices}{equation.3.12}{}}
\newlabel{eq13}{{13}{11}{Counting the vertices}{equation.3.13}{}}
\newlabel{eq14}{{14}{12}{Counting the vertices}{equation.3.14}{}}
\newlabel{eq15}{{15}{12}{Counting the vertices}{equation.3.15}{}}
\newlabel{eq16}{{16}{12}{Counting the vertices}{equation.3.16}{}}
\newlabel{eq17}{{17}{13}{Counting the vertices}{equation.3.17}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Counting the edges}{13}{subsection.3.3}}
\newlabel{eq18}{{18}{13}{Counting the edges}{equation.3.18}{}}
\newlabel{chv1}{{19}{14}{Counting the edges}{equation.3.19}{}}
\newlabel{chv2}{{20}{14}{Counting the edges}{equation.3.20}{}}
\newlabel{chv3}{{21}{14}{Counting the edges}{equation.3.21}{}}
\newlabel{chv4}{{22}{14}{Counting the edges}{equation.3.22}{}}
\newlabel{theorem5}{{5}{15}{}{theorem.5}{}}
\newlabel{eq23}{{23}{15}{}{equation.3.23}{}}
\newlabel{eq24}{{24}{15}{}{equation.3.24}{}}
\newlabel{eq25}{{25}{15}{}{equation.3.25}{}}
\newlabel{eq26}{{26}{15}{Counting the edges}{equation.3.26}{}}
\newlabel{eq27}{{27}{15}{Counting the edges}{equation.3.27}{}}
\newlabel{eq28}{{28}{15}{Counting the edges}{equation.3.28}{}}
\newlabel{eq29}{{29}{15}{Counting the edges}{equation.3.29}{}}
\newlabel{eq30}{{30}{16}{Counting the edges}{equation.3.30}{}}
\newlabel{eq31}{{31}{16}{Counting the edges}{equation.3.31}{}}
\newlabel{eq32}{{32}{16}{Counting the edges}{equation.3.32}{}}
\newlabel{eq33}{{33}{16}{Counting the edges}{equation.3.33}{}}
\newlabel{chv5}{{34}{17}{Counting the edges}{equation.3.34}{}}
\newlabel{theorem6}{{6}{17}{}{theorem.6}{}}
\newlabel{eq35}{{35}{17}{}{equation.3.35}{}}
\newlabel{eq36}{{36}{17}{}{equation.3.36}{}}
\newlabel{eq37}{{37}{17}{}{equation.3.37}{}}
\newlabel{eq38}{{38}{17}{}{equation.3.38}{}}
\newlabel{eq39}{{39}{17}{}{equation.3.39}{}}
\newlabel{eq40}{{40}{17}{}{equation.3.40}{}}
\newlabel{eq41}{{41}{18}{Counting the edges}{equation.3.41}{}}
\newlabel{eq42}{{42}{18}{Counting the edges}{equation.3.42}{}}
\newlabel{eq43}{{43}{18}{Counting the edges}{equation.3.43}{}}
\newlabel{eq44}{{44}{18}{Counting the edges}{equation.3.44}{}}
\newlabel{eq45}{{45}{18}{Counting the edges}{equation.3.45}{}}
\newlabel{eq46}{{46}{18}{Counting the edges}{equation.3.46}{}}
\newlabel{47}{{47}{18}{Counting the edges}{equation.3.47}{}}
\newlabel{48}{{48}{18}{Counting the edges}{equation.3.48}{}}
\newlabel{49}{{49}{18}{Counting the edges}{equation.3.49}{}}
\newlabel{50}{{50}{18}{Counting the edges}{equation.3.50}{}}
\newlabel{eq51}{{51}{19}{Counting the edges}{equation.3.51}{}}
\newlabel{eq52}{{52}{19}{Counting the edges}{equation.3.52}{}}
\newlabel{theorem7}{{7}{19}{}{theorem.7}{}}
\newlabel{chv6}{{56}{20}{Counting the edges}{equation.3.56}{}}
\newlabel{eq57}{{57}{20}{Counting the edges}{equation.3.57}{}}
\newlabel{theorem8}{{8}{20}{}{theorem.8}{}}
\newlabel{eq58}{{58}{20}{}{equation.3.58}{}}
\newlabel{eq59}{{59}{20}{}{equation.3.59}{}}
\newlabel{eq60}{{60}{20}{}{equation.3.60}{}}
\newlabel{eq61}{{61}{20}{}{equation.3.61}{}}
\newlabel{eq62}{{62}{21}{Counting the edges}{equation.3.62}{}}
\newlabel{eq63}{{63}{21}{Counting the edges}{equation.3.63}{}}
\newlabel{eq64}{{64}{21}{Counting the edges}{equation.3.64}{}}
\newlabel{eq65}{{65}{21}{Counting the edges}{equation.3.65}{}}
\newlabel{eq66}{{66}{21}{Counting the edges}{equation.3.66}{}}
\newlabel{eq67}{{67}{21}{Counting the edges}{equation.3.67}{}}
\newlabel{eq68}{{68}{21}{Counting the edges}{equation.3.68}{}}
\newlabel{chv7}{{69}{22}{Counting the edges}{equation.3.69}{}}
\newlabel{chv8}{{70}{22}{Counting the edges}{equation.3.70}{}}
\newlabel{chv9}{{71}{22}{Counting the edges}{equation.3.71}{}}
\newlabel{chv10}{{72}{22}{Counting the edges}{equation.3.72}{}}
\newlabel{theorem9}{{9}{22}{}{theorem.9}{}}
\newlabel{eq73}{{73}{23}{}{equation.3.73}{}}
\newlabel{74}{{74}{23}{}{equation.3.74}{}}
\newlabel{75}{{75}{23}{}{equation.3.75}{}}
\newlabel{eq76}{{76}{23}{}{equation.3.76}{}}
\newlabel{eq77}{{77}{23}{}{equation.3.77}{}}
\newlabel{eq78}{{78}{23}{}{equation.3.78}{}}
\newlabel{eq79}{{79}{23}{}{equation.3.79}{}}
\newlabel{eq80}{{80}{24}{Counting the edges}{equation.3.80}{}}
\newlabel{81}{{81}{24}{Counting the edges}{equation.3.81}{}}
\newlabel{eq82}{{82}{24}{Counting the edges}{equation.3.82}{}}
\newlabel{eq83}{{83}{24}{Counting the edges}{equation.3.83}{}}
\newlabel{eq84}{{84}{24}{Counting the edges}{equation.3.84}{}}
\newlabel{eq85}{{85}{24}{Counting the edges}{equation.3.85}{}}
\newlabel{eq86}{{86}{24}{Counting the edges}{equation.3.86}{}}
\newlabel{eq87}{{87}{24}{Counting the edges}{equation.3.87}{}}
\newlabel{eq88}{{88}{24}{Counting the edges}{equation.3.88}{}}
\newlabel{eq89}{{89}{24}{Counting the edges}{equation.3.89}{}}
\newlabel{eq90}{{90}{24}{Counting the edges}{equation.3.90}{}}
\newlabel{91}{{91}{24}{Counting the edges}{equation.3.91}{}}
\bibcite{Albuquerque2009a}{1}
\bibcite{bartholdi}{2}
\bibcite{Be}{3}
\bibcite{Ca1}{4}
\newlabel{eq92}{{92}{25}{Counting the edges}{equation.3.92}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Acknowledgment}{25}{section.4}}
\bibcite{Ca2}{5}
\bibcite{Floyd}{6}
\bibcite{harpe}{7}
\bibcite{Hu}{8}
\bibcite{BFP}{9}
\bibcite{Brandani2006}{10}
\bibcite{Sullivan}{11}
\bibcite{Ungerboeck1987}{12}