Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More Torsion in the Homology of the Matching Complex   A matching on a set $X$ is a collection of pairwise disjoint subsets of $X$
of size two. Using computers, we analyze the integral homology of the matching
complex $M_n$, which is the simplicial complex of matchings on the set $\{1,
>..., n\}$. The main result is the detection of elements of order $p$ in the
homology for $p \in \{5,7,11,13\}$. Specifically, we show that there are
elements of order 5 in the homology of $M_n$ for $n \ge 18$ and for $n \in
{14,16}$. The only previously known value was $n = 14$, and in this particular
case we have a new computer-free proof. Moreover, we show that there are
elements of order 7 in the homology of $M_n$ for all odd $n$ between 23 and 41
and for $n=30$. In addition, there are elements of order 11 in the homology of
$M_{47}$ and elements of order 13 in the homology of $M_{62}$. Finally, we
compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of
$H_d(M_n;Z)$ for $13 \le n \le 16$; a complete description of the homology
already exists for $n \le 12$. To prove the results, we use a
representation-theoretic approach, examining subcomplexes of the chain complex
of $M_n$ obtained by letting certain groups act on the chain complex.

6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg