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Asymptotic Enumeration of Constellations and Related Families of Maps on Orientable Surfaces

Published online by Cambridge University Press:  01 July 2009

GUILLAUME CHAPUY
GUILLAUME CHAPUY*
Affiliation:
Laboratoire d'Informatique de l'École Polytechnique, 91128 Palaiseau Cedex, France (e-mail: [email protected])
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Abstract

We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces: m-hypermaps and m-constellations. For m = 2 they correspond respectively to maps with even face degrees and bipartite maps. We obtain explicit asymptotic formulas for the number of such maps with any finite set of allowed face degrees.

Our proofs combine a bijective approach, generating series techniques related to lattice walks, and elementary algebraic graph theory.

A special case of our results implies former conjectures of Z. Gao.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 4 , July 2009 , pp. 477 - 516
Copyright
Copyright © Cambridge University Press 2009

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