1Institut de Physique Théorique, CEA, IPhT, F-91191 Gif-sur-Yvette, CNRS, URA 2306 and Département de Mathématiques et Applications, École normale supérieure, 45 rue d’Ulm, F-75231 Paris Cedex 05 2Institut de Physique Théorique, CEA, IPhT, F-91191 Gif-sur-Yvette, CNRS, URA 2306
The electronic journal of combinatorics, Tome 21 (2014) no. 1
We derive a formula for the generating function of $d$-irreducible bipartite planar maps with several boundaries, i.e. having several marked faces of controlled degrees. It extends a formula due to Collet and Fusy for the case of arbitrary (non necessarily irreducible) bipartite planar maps, which is recovered by taking $d=0$. As an application, we obtain an expression for the number of $d$-irreducible bipartite planar maps with a prescribed number of faces of each allowed degree. Very explicit expressions are given in the case of maps without multiple edges ($d=2$), $4$-irreducible maps and maps of girth at least $6$ ($d=4$). Our derivation is based on a tree interpretation of the various encountered generating functions.
1
Institut de Physique Théorique,
CEA, IPhT, F-91191 Gif-sur-Yvette,
CNRS, URA 2306
and
Département de Mathématiques et Applications,
École normale supérieure, 45 rue d’Ulm, F-75231 Paris Cedex 05
2
Institut de Physique Théorique,
CEA, IPhT, F-91191 Gif-sur-Yvette,
CNRS, URA 2306
@article{10_37236_3443,
author = {J. Bouttier and E. Guitter},
title = {A note on irreducible maps with several boundaries},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3443},
zbl = {1300.05070},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3443/}
}
TY - JOUR
AU - J. Bouttier
AU - E. Guitter
TI - A note on irreducible maps with several boundaries
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3443/
DO - 10.37236/3443
ID - 10_37236_3443
ER -
%0 Journal Article
%A J. Bouttier
%A E. Guitter
%T A note on irreducible maps with several boundaries
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3443/
%R 10.37236/3443
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J. Bouttier; E. Guitter. A note on irreducible maps with several boundaries. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3443
