Publication : t13/076

A note on irreducible maps with several boundaries

Bouttier J. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Guitter E. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Abstract:
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 we recover 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.
Année de publication : 2014
Revue : Electr. J. Combin. 21 #P1.23 (2014)
Preprint : arXiv:1305.4816
Lien : http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i1p23
Langue : Anglais

 

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