\relax 
\citation{McKay90}
\citation{McWo90}
\citation{ChMiSa05}
\citation{Gessel90}
\citation{ChMiSa05}
\citation{Macdonald95}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Introduction}}{1}}
\newlabel{eq:allgraphs}{{1}{1}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Symmetric series and D-finiteness}}{1}}
\citation{Gessel90}
\citation{GoJaRe83}
\citation{Stanley99}
\citation{Gessel90}
\newlabel{eq:scalp}{{2}{2}}
\newlabel{thm:theta}{{1.1}{2}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{D-finite multivariate series}}{2}}
\citation{Lipshitz88}
\citation{ChMiSa05}
\citation{ChMiSa05}
\citation{GoJaRe83}
\citation{BeLaLe98}
\citation{Joyal81}
\citation{BeLaLe98}
\citation{BeLaLe98}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{D-finite symmetric series}}{3}}
\newlabel{thm:rsc_pres_df}{{1.2}{3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Effective calculation and algorithms}}{3}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{D-finite symmetric series appear naturally in combinatorics}}{3}}
\newlabel{eq:cycle_index}{{3}{3}}
\citation{Stanley80}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Index series of small species and their corresponding symmetric functions}}{4}}
\newlabel{tab:smallspec}{{1}{4}}
\newlabel{thm:Dfin_species}{{2.1}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The graph associated to the coloured set partition $\{ \{1_3,4_2\}, \{2_2,6_4\},\{3_4,7_3\},\{5_2,8_1\}\}$}}{5}}
\newlabel{fig:graph}{{1}{5}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Using species to describe regular graph-like structures}}{5}}
\citation{BeCa78}
\citation{McWo90}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A structure composed of a set of smaller structures (cycles and 3-sets).}}{6}}
\newlabel{fig:multi}{{2}{6}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{$S$-regular graphs}}{6}}
\citation{DeJa82}
\citation{Comtet68}
\citation{Comtet68}
\citation{Bender74a}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Counting sequences for $\{i,j\}$-regular graphs for small values of\nonbreakingspace $i$ and\nonbreakingspace $j$.}}{7}}
\newlabel{tab:kjreg}{{2}{7}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{Set covers and uniform hypergraphs}}{7}}
\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}
\citation{ChMiSa05}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Asymptotic analysis}}{8}}
\newlabel{sec:asympt}{{4}{8}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{Technique}}{8}}
\citation{Sloane}
\citation{Flajolet87}
\@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 $n$.}}{9}}
\newlabel{tab:graph}{{3}{9}}
\citation{WiZe85}
\citation{ChMiSa05}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Asymptotic enumeration of different classes of regular objects}}{10}}
\newlabel{tab:other}{{4}{10}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Comments, conclusions and perspectives}}{10}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Asymptotic expansions of different families of functions}}{10}}
\citation{Mishna03}
\citation{MBM06}
\citation{FlGeSa05}
\bibstyle{acm}
\bibcite{Bender74a}{1}
\bibcite{BeCa78}{2}
\bibcite{BeLaLe98}{3}
\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}
\newlabel{sec:conclusion}{{5.2}{11}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{D-finite species?}}{11}}
\newlabel{eq:cis1}{{1}{11}}
\newlabel{eq:cis2}{{2}{11}}
\newlabel{eq:cis3}{{3}{11}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{}{Acknowledgements}}{11}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{11}}
\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}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{29.38873pt}
\newlabel{tocindent3}{0pt}
