Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gluing of Surfaces with Polygonal Boundaries   By pairwise gluing of edges of a polygon, one produces two-dimensional
surfaces with handles and boundaries. In this paper, we count the number ${\cal
N}_{g,L}(n_1, n_2, ..., n_L)$ of different ways to produce a surface of given
genus $g$ with $L$ polygonal boundaries with given numbers of edges $n_1, n_2,
>..., n_L$. Using combinatorial relations between graphs on real
two-dimensional surfaces, we derive recursive relations between ${\cal
N}_{g,L}$. We show that Harer-Zagier numbers appear as a particular case of
${\cal N}_{g,L}$ and derive a new explicit expression for them.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg