A combinatorial relationship between Eulerian maps and hypermaps in orientable surfaces
type: Item
instance of: scholarly article
title: A combinatorial relationship between Eulerian maps and hypermaps in orientable surfaces
zbMATH Open document ID: 0949.05019
published in: Journal of Combinatorial Theory. Series A
publication date: 2000-11-29T00:00:00Z
review text: This paper studies maps, graphs cellularly embedded on orientable surfaces. The genus series is the generating function \(M(u,x,y,z)\) where the coefficient on \(u^g x^i y^j z^k\) is the number \(m_{g,i,j,k}\) of rooted maps of genus \(g\) with \(i\) vertices, \(j\) faces, and \(k\) edges (any one of these parameters is superfluous, but all are included for symmetry). Using character theory the authors had previously determined an interesting relationship between the genus series for rooted maps and the genus series for rooted quadrangulations. The authors generalize this relationship to a larger set of maps where the relationship can be described. They examine properties of a putative bijection.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 1319934
zbMATH Keywords: orientable surfaces
zbMATH Keywords: genus series
zbMATH Keywords: rooted maps
author: David M. Jackson
author: Terry I. Visentin
reviewed by: Dan S. Archdeacon
MaRDI profile type: Publication
full work available at URL: jcta.1998.2951
OpenAlex ID: W2066624456
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DOI: 10.1006/JCTA.1998.2951
description: scientific article; zbMATH DE number 1319934