Geodesic
Airy phenomena and analytic combinatorics of connected graphs
The electronic journal of combinatorics, Tome 11 (2004) no. 1

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl EuDML
Until now, the enumeration of connected graphs has been dealt with by probabilistic methods, by special combinatorial decompositions or by somewhat indirect formal series manipulations. We show here that it is possible to make analytic sense of the divergent series that expresses the generating function of connected graphs. As a consequence, it becomes possible to derive analytically known enumeration results using only first principles of combinatorial analysis and straight asymptotic analysis—specifically, the saddle-point method. In this perspective, the enumeration of connected graphs by excess (of number of edges over number of vertices) derives from a simple saddle-point analysis. Furthermore, a refined analysis based on coalescent saddle points yields complete asymptotic expansions for the number of graphs of fixed excess, through an explicit connection with Airy functions.
DOI : 10.37236/1787
Classification : 05C30, 05A15, 05A16, 05C40, 05C80
Mots-clés : enumeration, connected graphs, saddle-point method 
Philippe Flajolet; Bruno Salvy; Gilles Schaeffer. Airy phenomena and analytic combinatorics of connected graphs. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1787
@article{10_37236_1787,
     author = {Philippe Flajolet and Bruno Salvy and Gilles Schaeffer},
     title = {Airy phenomena and analytic combinatorics of connected graphs},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1787},
     zbl = {1053.05064},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1787/}
}
TY  - JOUR
AU  - Philippe Flajolet
AU  - Bruno Salvy
AU  - Gilles Schaeffer
TI  - Airy phenomena and analytic combinatorics of connected graphs
JO  - The electronic journal of combinatorics
PY  - 2004
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1787/
DO  - 10.37236/1787
ID  - 10_37236_1787
ER  - 
%0 Journal Article
%A Philippe Flajolet
%A Bruno Salvy
%A Gilles Schaeffer
%T Airy phenomena and analytic combinatorics of connected graphs
%J The electronic journal of combinatorics
%D 2004
%V 11
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/1787/
%R 10.37236/1787
%F 10_37236_1787

Cité par Sources :