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A THEORY OF RESTRICTED REGULARITY OF HYPERMAPS
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 Title & Authors
A THEORY OF RESTRICTED REGULARITY OF HYPERMAPS
Dazevedo Antonio Breda;
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 Abstract
Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product . In this correspondence, hypermaps correspond to conjugacy classes of subgroups of , and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out of the triangle group . This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups of of finite index. This generalises the notion of regularity to some non-regular objects.
 Keywords
hypermaps;maps;hypergraphs;regularity;restricted regularity;orientably regular;
 Language
English
 Cited by
1.
Map operations and k-orbit maps, Journal of Combinatorial Theory, Series A, 2010, 117, 4, 411  crossref(new windwow)
2.
On chirality groups and regular coverings of regular oriented hypermaps, Czechoslovak Mathematical Journal, 2011, 61, 4, 1037  crossref(new windwow)
3.
Regular pseudo-oriented maps and hypermaps of low genus, Discrete Mathematics, 2015, 338, 6, 895  crossref(new windwow)
4.
Vertex-transitive maps with Schläfli type, Discrete Mathematics, 2014, 317, 53  crossref(new windwow)
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