Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trees, homology, and automorphism groups of RAAGs   We study the homology of an explicit finite-index subgroup of the
automorphism group of a partially commutative group, in the case when its
defining graph is a tree. More concretely, we give a lower bound on the first
Betti number of this subgroup, based on the number and degree of a certain type
of vertices, which we call deep. We then use combinatorial methods to analyze
the average value of this Betti number, in terms of the size of the defining
tree.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc