Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The commuting complex of the symmetric group with bounded number of
  $p$-cycles   For a fixed prime $p$, we consider a filtration of the commuting complex of
elements of order $p$ in the symmetric group $\mathfrak{S}_n$. The filtration
is obtained by imposing successively relaxed bounds on the number of disjoint
$p$-cycles in the cycle decomposition of the elements. We show that each term
in the filtration becomes highly acyclic as $n$ increases. We use
$\mathbf{FI}$-modules in the proof.

13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga