Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic analysis of $k$-noncrossing matchings   In this paper we study $k$-noncrossing matchings. A $k$-noncrossing matching
is a labeled graph with vertex set $\{1,...,2n\}$ arranged in increasing order
in a horizontal line and vertex-degree 1. The $n$ arcs are drawn in the upper
halfplane subject to the condition that there exist no $k$ arcs that mutually
intersect. We derive: (a) for arbitrary $k$, an asymptotic approximation of the
exponential generating function of $k$-noncrossing matchings $F_k(z)$. (b) the
asymptotic formula for the number of $k$-noncrossing matchings $f_{k}(n) \sim
c_k n^{-((k-1)^2+(k-1)/2)} (2(k-1))^{2n}$ for some $c_k>0$.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga