Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655284 | Journal of Combinatorial Theory, Series A | 2014 | 21 Pages |
Abstract
Constellations and hypermaps generalize combinatorial maps, i.e., embeddings of graphs in a surface, in terms of factorizations of permutations. In this paper, we extend a result of Jackson and Visentin (1990) stating an enumerative relation between quadrangulations and bipartite quadrangulations. We show a similar relation between hypermaps and constellations by using a result of Littlewood on factorization of characters. A combinatorial proof of Littlewood's result is also given. Furthermore, we show that the coefficients in our relation are all positive integers, hinting at the possibility of a combinatorial interpretation. Using this enumerative relation, we recover a result on the asymptotic behavior of hypermaps obtained by Chapuy (2009).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Wenjie Fang,