Wenjie Fang - A generalization of the quadrangulation relation to constellations and hypermaps

dmtcs:12789 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12789
A generalization of the quadrangulation relation to constellations and hypermapsArticle

Authors: Wenjie Fang ORCID1

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).


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: combinatorial maps,constellations,enumeration,character factorization,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Interactions Of Combinatorics; Funder: French National Research Agency (ANR); Code: ANR-08-JCJC-0011

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