Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality index of oriented regular hypermaps   By adapting the notion of chirality group, the duality group of $\cal H$ can
be defined as the the minimal subgroup $D({\cal H}) \trianglelefteq Mon({\cal
H})$ such that ${\cal H}/D({\cal H})$ is a self-dual hypermap (a hypermap
isomorphic to its dual). Here, we prove that for any positive integer $d$, we
can find a hypermap of that duality index (the order of $D({\cal H})$), even
when some restrictions apply, and also that, for any positive integer $k$, we
can find a non self-dual hypermap such that $|Mon({\cal H})|/d=k$. This $k$
will be called the \emph{duality coindex} of the hypermap.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
19
The categories of this paper are: eess