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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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https://hal.inria.fr/hal-01229720
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Submitted on : Tuesday, November 17, 2015 - 10:20:33 AM
Last modification on : Tuesday, September 22, 2020 - 3:51:14 AM
Long-term archiving on: : Thursday, February 18, 2016 - 11:43:42 AM

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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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