A THEORY OF RESTRICTED REGULARITY OF HYPERMAPS

Title & Authors
A THEORY OF RESTRICTED REGULARITY OF HYPERMAPS
Dazevedo Antonio Breda;

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 $\small{\Delta=C_2*C_2*C_2}$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\small{\Delta}$, 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$\small{(\Delta)}$ of the triangle group $\small{\Delta}$. 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 $\small{\Theta}$ of $\small{\Delta}$ 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
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On chirality groups and regular coverings of regular oriented hypermaps, Czechoslovak Mathematical Journal, 2011, 61, 4, 1037
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Regular pseudo-oriented maps and hypermaps of low genus, Discrete Mathematics, 2015, 338, 6, 895
4.
Vertex-transitive maps with Schläfli type, Discrete Mathematics, 2014, 317, 53
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