Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Parabolic Double Cosets in Symmetric Groups   Billey, Konvalinka, Petersen, Solfstra, and Tenner recently presented a
method for counting parabolic double cosets in Coxeter groups, and used it to
compute $p_n$, the number of parabolic double cosets in $S_n$, for $n\leq13$.
In this paper, we derive a new formula for $p_n$ and an efficient polynomial
time algorithm for evaluating this formula. We use these results to compute
$p_n$ for $n\leq5000$ and to prove an asymptotic formula for $p_n$ that was
conjectured by Billey et al.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom