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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
Affiliation:
Laboratoire d'Informatique de l'École Polytechnique, 91128 Palaiseau Cedex, France (e-mail: guillaume.chapuy@lix.polytechnique.fr)
Corresponding

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.


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Copyright © Cambridge University Press 2009

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