Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of the quadrangulation relation to constellations and
  hypermaps   Constellations and hypermaps generalize combinatorial maps, 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) 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 coefficients in
our relation are all positive integers, hinting possibility of a combinatorial
interpretation. Using this enumerative relation, we recover a result on the
asymptotic behavior of hypermaps in Chapuy (2009).

7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph