# A generalization of the quadrangulation relation to constellations and hypermaps

Abstract : Constellations and hypermaps generalize combinatorial maps, $\textit{i.e.}$ embedding of graphs in a surface, in terms of factorization of permutations. In this paper, we extend a result of Jackson and Visentin (1990) on an enumerative relation between quadrangulations and bipartite quadrangulations. We show a similar relation between hypermaps and constellations by generalizing a result in the original paper on factorization of characters. Using this enumerative relation, we recover a result on the asymptotic behavior of hypermaps of Chapuy (2009).
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Conference papers

https://hal.inria.fr/hal-01229720
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• HAL Id : hal-01229720, version 1

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Wenjie Fang. A generalization of the quadrangulation relation to constellations and hypermaps. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.13-24. ⟨hal-01229720⟩

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