Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Counting and Asymptotics of $k$-noncrossing tangled-diagrams   In this paper we enumerate $k$-noncrossing tangled-diagrams. A
tangled-diagram is a labeled graph whose vertices are $1,...,n$ have degree
$\le 2$, and are arranged in increasing order in a horizontal line. Its arcs
are drawn in the upper halfplane with a particular notion of crossings and
nestings. Our main result is the asymptotic formula for the number of
$k$-noncrossing tangled-diagrams $T_{k}(n) \sim c_k n^{-((k-1)^2+(k-1)/2)}
(4(k-1)^2+2(k-1)+1)^n$ for some $c_k>0$.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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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: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: physics
34
The categories of this paper are: chem-ph