Algebraic hypermap morphisms
type: Item
instance of: scholarly article
title: Algebraic hypermap morphisms
zbMATH Open document ID: 0983.20002
author: Leonardo Cangelmi
author: Paola Cellini
published in: European Journal of Combinatorics
publication date: 2002-01-16T00:00:00Z
review text: Algebraic hypermaps combinatorially describe topological hypermaps, that is, embeddings of hypergraphs in compact orientable surfaces. For any set \(\Omega\) denote by \(\text{Sym}(\Omega)\) the group of all permutations of \(\Omega\). An algebraic hypermap \(H\) is a triple \((\Omega,\sigma,\alpha)\), where \(\Omega\) is a finite set, \(\sigma,\alpha\in\text{Sym}(\Omega)\), and the group \(\langle\sigma,\alpha\rangle\) generated by \(\sigma\) and \(\alpha\) is transitive on \(\Omega\). In this paper the authors introduce hypermap morphisms, a natural notion of degree and brach number of hypermap morphisms. Theorem 1.1. Let \(\Phi\colon H\to H'\) be a hypermap morphism with degree \(m\) and branch number \(B\). Let \(g\) and \(g'\) be the genera of \(H\) and \(H'\), respectively. Then \(2g-2=m(2g'-2)+B\).
reviewed by: V. V. Chueshev
Mathematics Subject Classification ID: 20B20
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20B05
zbMATH DE Number: 1512030
zbMATH Keywords: algebraic hypermaps
zbMATH Keywords: compact orientable surfaces
zbMATH Keywords: groups of permutations
zbMATH Keywords: transitive permutation groups
MaRDI profile type: Publication
OpenAlex ID: W2005137666
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DOI: 10.1006/EUJC.1999.0389
description: scientific article; zbMATH DE number 1512030