Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of double cosets and fundamental domains for the subgroups
  of the modular group   As noticed by R. Kulkarni, the conjugacy classes of subgroups of the modular
group correspond bijectively to bipartite cuboid graphs. We'll explain how to
recover the graph corresponding to a subgroup $G$ of
$\mathrm{PSL}_2(\mathbb{Z})$ from the combinatorics of the right action of
$\mathrm{PSL}_2(\mathbb{Z})$ on the right cosets
$G\setminus\mathrm{PSL}_2(\mathbb{Z})$. This gives a method of constructing
nice fundamental domains (which Kulkarni calls "special polygons") for the
action of $G$ on the upper half plane. For the classical congruence subgroups
$\Gamma_0(N)$, $\Gamma_1(N)$, $\Gamma(N)$ etc. the number of operations the
method requires is the index times something that grows not faster than a
polynomial in $\log N$. We also give algorithms to locate a given element of
the upper half-plane on the fundamental domain and to write a given element of
$G$ as a product of independent generators.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org