Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bipartite-uniform hypermaps on the sphere   A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured
in such a way that ``neighbouring'' hypervertices have different colours. It is
bipartite-uniform if within each of the sets of hypervertices of the same
colour, hyperedges and hyperfaces, elements have common valencies. The flags of
a bipartite hypermap are naturally 2-coloured by assigning the colour of its
adjacent hypervertices. A hypermap is bipartite-regular if the automorphism
group acts transitively on each set of coloured flags. If the automorphism
group acts transitively on the set of all flags, the hypermap is regular. In
this paper we classify the bipartite-uniform hypermaps on the sphere (up to
duality). Two constructions of bipartite-uniform hypermaps are given. All
bipartite-uniform spherical hypermaps are shown to be constructed in this way.
As a by-product we show that every bipartite-uniform hypermap on the sphere is
bipartite-regular. We also compute their irregularity group and index, and also
their closure cover and covering core.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph