Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using recurrence relations to count in symmetric groups   We use the fact that certain cosets of the stabilizer of points are pairwise
conjugate in a symmetric group $S_n$ in order to construct recurrence relations
for enumerating certain subsets of $S_n$. Occasionally one can find `closed
form' solutions to such recurrence relations. For example, the probability that
a random element of $S_n$ has no cycle of length divisible by $q$ is
$\prod_{d=1}^{\lfloor n/q\rfloor} (1-\frac{1}{dq})$.

25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph