\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{McKay90}
\citation{McWo90}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{eq:allgraphs}{{1}{1}{Introduction}{equation.1.1}{}}
\citation{ChMiSa05}
\citation{Gessel90}
\citation{ChMiSa05}
\citation{Macdonald95}
\@writefile{toc}{\contentsline {section}{\numberline {2}Symmetric series and D-finiteness}{2}{section.2}}
\citation{Gessel90}
\citation{GoJaRe83}
\citation{Stanley99}
\citation{Gessel90}
\newlabel{eq:scalp}{{2}{3}{Symmetric series and D-finiteness}{equation.2.2}{}}
\newlabel{thm:theta}{{2.1}{3}{Gessel\cite {Gessel90}; Goulden \& Jackson\cite {GoJaRe83}}{thm.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}D-finite multivariate series}{3}{subsection.2.1}}
\citation{Lipshitz88}
\citation{ChMiSa05}
\citation{ChMiSa05}
\citation{GoJaRe83}
\citation{BeLaLe98}
\citation{Joyal81}
\citation{BeLaLe98}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}D-finite symmetric series}{4}{subsection.2.2}}
\newlabel{thm:rsc_pres_df}{{2.2}{4}{Gessel}{thm.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Effective calculation and algorithms}{4}{subsection.2.3}}
\@writefile{toc}{\contentsline {section}{\numberline {3}D-finite symmetric series appear naturally in combinatorics}{4}{section.3}}
\citation{BeLaLe98}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Index series of small species and their corresponding symmetric functions}}{5}{table.1}}
\newlabel{tab:smallspec}{{1}{5}{Index series of small species and their corresponding symmetric functions}{table.1}{}}
\newlabel{eq:cycle_index}{{3}{5}{D-finite symmetric series appear naturally in combinatorics}{equation.3.3}{}}
\citation{Stanley80}
\newlabel{thm:Dfin_species}{{3.1}{6}{}{thm.3.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Using species to describe regular graph-like structures}{7}{section.4}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The graph associated with the colored set partition $\{ \{1_3,4_2\}, \{2_2,6_4\},\{3_4,7_3\},\{5_2,8_1\}\}$}}{8}{figure.1}}
\newlabel{fig:graph}{{1}{8}{The graph associated with the colored set partition $\{ \{1_3,4_2\}, \{2_2,6_4\},\{3_4,7_3\},\{5_2,8_1\}\}$}{figure.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A structure composed of a set of smaller structures (cycles and 3-sets).}}{8}{figure.2}}
\newlabel{fig:multi}{{2}{8}{A structure composed of a set of smaller structures (cycles and 3-sets)}{figure.2}{}}
\citation{BeCa78}
\citation{McWo90}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Counting sequences for $\{i,j\}$-regular graphs for small values of\nobreakspace  {}$i$ and\nobreakspace  {}$j$.}}{9}{table.2}}
\newlabel{tab:kjreg}{{2}{9}{Counting sequences for $\{i,j\}$-regular graphs for small values of~$i$ and~$j$}{table.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}$S$-regular graphs}{9}{subsection.4.1}}
\citation{DeJa82}
\citation{Comtet68}
\citation{Comtet68}
\citation{Bender74a}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Set covers and uniform hypergraphs}{10}{subsection.4.2}}
\citation{Gropp92}
\citation{Read58}
\citation{Read60}
\citation{BeCa78}
\citation{McKay90}
\citation{McWo91}
\citation{Bollobas80}
\citation{McKay90}
\citation{McWa03}
\citation{McWo91}
\citation{BeCa78}
\citation{Bollobas82}
\citation{Gessel90}
\citation{Domocos96}
\@writefile{toc}{\contentsline {section}{\numberline {5}Asymptotic analysis}{11}{section.5}}
\newlabel{sec:asympt}{{5}{11}{Asymptotic analysis}{section.5}{}}
\citation{ChMiSa05}
\citation{Sloane}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Technique}{12}{subsection.5.1}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces  Asymptotic enumeration formulas for different classes of $k$-regular graphs. Formulas for 1- and 3- regular are valid only for even $n$.}}{13}{table.3}}
\newlabel{tab:graph}{{3}{13}{Asymptotic enumeration formulas for different classes of $k$-regular graphs. Formulas for 1- and 3- regular are valid only for even $n$}{table.3}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Asymptotic enumeration of different classes of regular objects}}{13}{table.4}}
\newlabel{tab:other}{{4}{13}{Asymptotic enumeration of different classes of regular objects}{table.4}{}}
\citation{Flajolet87}
\citation{WiZe85}
\citation{ChMiSa05}
\@writefile{toc}{\contentsline {section}{\numberline {6}Comments, conclusions and perspectives}{14}{section.6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Asymptotic expansions of different families of functions}{14}{subsection.6.1}}
\citation{Mishna03}
\citation{MBM06}
\citation{FlGeSa05}
\bibcite{Bender74a}{1}
\bibcite{BeCa78}{2}
\bibcite{BeLaLe98}{3}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}D-finite species?}{15}{subsection.6.2}}
\newlabel{sec:conclusion}{{6.2}{15}{D-finite species?}{subsection.6.2}{}}
\newlabel{eq:cis1}{{1}{15}{D-finite species?}{Item.5}{}}
\newlabel{eq:cis2}{{2}{15}{D-finite species?}{Item.6}{}}
\newlabel{eq:cis3}{{3}{15}{D-finite species?}{Item.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Acknowledgements}{15}{section.7}}
\bibcite{Bollobas80}{4}
\bibcite{Bollobas82}{5}
\bibcite{MBM06}{6}
\bibcite{ChMiSa05}{7}
\bibcite{Comtet68}{8}
\bibcite{Beckenbach64}{9}
\bibcite{DeJa82}{10}
\bibcite{Domocos96}{11}
\bibcite{Flajolet87}{12}
\bibcite{FlGeSa05}{13}
\bibcite{Gessel90}{14}
\bibcite{GoJaRe83}{15}
\bibcite{Gropp92}{16}
\bibcite{Joyal81}{17}
\bibcite{Lipshitz88}{18}
\bibcite{Macdonald95}{19}
\bibcite{McKay90}{20}
\bibcite{McWa03}{21}
\bibcite{McWo90}{22}
\bibcite{McWo91}{23}
\bibcite{Mishna03}{24}
\bibcite{Read58}{25}
\bibcite{Read60}{26}
\bibcite{Sloane}{27}
\bibcite{Stanley80}{28}
\bibcite{Stanley99}{29}
\bibcite{WiZe85}{30}
