Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-dimensional maps and subgroup growth   In this paper we derive a generating series for the number of cellular
complexes known as pavings or three-dimensional maps, on $n$ darts, thus
solving an analogue of Tutte's problem in dimension three.
  The generating series we derive also counts free subgroups of index $n$ in
$\Delta^+ = \mathbb{Z}_2*\mathbb{Z}_2*\mathbb{Z}_2$ via a simple bijection
between pavings and finite index subgroups which can be deduced from the action
of $\Delta^+$ on the cosets of a given subgroup. We then show that this
generating series is non-holonomic. Furthermore, we provide and study the
generating series for isomorphism classes of pavings, which correspond to
conjugacy classes of free subgroups of finite index in $\Delta^+$.
  Computational experiments performed with software designed by the authors
provide some statistics about the topology and combinatorics of pavings on
$n\leq 16$ darts.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics