Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic distribution of fixed points of pattern-avoiding involutions   For a variety of pattern-avoiding classes, we describe the limiting
distribution for the number of fixed points for involutions chosen uniformly at
random from that class. In particular we consider monotone patterns of
arbitrary length as well as all patterns of length 3. For monotone patterns we
utilize the connection with standard Young tableaux with at most $k$ rows and
involutions avoiding a monotone pattern of length $k$. For every pattern of
length 3 we give the bivariate generating function with respect to fixed points
for the involutions that avoid that pattern, and where applicable apply tools
from analytic combinatorics to extract information about the limiting
distribution from the generating function. Many well-known distributions
appear.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph