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Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2014

A note on irreducible maps with several boundaries

Résumé

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.

Dates et versions

hal-00871941 , version 1 (11-10-2013)

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Jérémie Bouttier, Emmanuel Guitter. A note on irreducible maps with several boundaries. The Electronic Journal of Combinatorics, 2014, 21 (1), pp.P1.23. ⟨hal-00871941⟩
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