Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unified bijections for planar hypermaps with general cycle-length
  constraints   We present a general bijective approach to planar hypermaps with two main
results. First we obtain unified bijections for all classes of maps or
hypermaps defined by face-degree constraints and girth constraints. To any such
class we associate bijectively a class of plane trees characterized by local
constraints. This unifies and greatly generalizes several bijections for maps
and hypermaps. Second, we present yet another level of generalization of the
bijective approach by considering classes of maps with non-uniform girth
constraints. More precisely, we consider "well-charged maps", which are maps
with an assignment of "charges" (real numbers) on vertices and faces, with the
constraints that the length of any cycle of the map is at least equal to the
sum of the charges of the vertices and faces enclosed by the cycle. We obtain a
bijection between charged hypermaps and a class of plane trees characterized by
local constraints.

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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: cs