Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting non-crossing permutations on surfaces of any genus   Given a surface with boundary and some points on its boundary, a polygon
diagram is a way to connect those points as vertices of non-overlapping
polygons on the surface. Such polygon diagrams represent non-crossing
permutations on a surface with any genus and number of boundary components. If
only bigons are allowed, then it becomes an arc diagram. The count of arc
diagrams is known to have a rich structure. We show that the count of polygon
diagrams exhibits the same interesting behaviours, in particular it is almost
polynomial in the number of points on the boundary components, and the leading
coefficients of those polynomials are the intersection numbers on the
compactified moduli space of curves.

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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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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: comp-gas
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The categories of this paper are: bayes-an