Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of 3-regular one-face maps on orientable or non-orientable
  surface up to all symmetries   We obtain explicit formulas for enumerating $3$-regular one-face maps on
orientable and non-orientable surfaces of a given genus $g$ up to all
symmetries. We use recent analytical results obtained by Bernardi and Chapuy
for counting rooted precubic maps on non-orientable surfaces together with more
widely known formulas for counting precubic maps on orientable surfaces. To
take into account all symmetries we use a result of Krasko and Omelchenko that
allows to reduce this problem to the problem of counting rooted quotient maps
on orbifolds.

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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: atom-ph