Surfaces having no regular hypermaps

Stephen E Wilson, Antonio Breda D'Azevedo

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

Original languageEnglish (US)
Pages (from-to)241-274
Number of pages34
JournalDiscrete Mathematics
Volume277
Issue number1-3
DOIs
StatePublished - Feb 28 2004

Fingerprint

Symmetry Group
Regular Map
Non-orientable Surface
Equivalence relation
Genus
Diagram
Theorem
Observation

Keywords

  • Graphs imbeddings
  • Hypermaps
  • Maps
  • Non-orientable surfaces

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Surfaces having no regular hypermaps. / Wilson, Stephen E; Breda D'Azevedo, Antonio.

In: Discrete Mathematics, Vol. 277, No. 1-3, 28.02.2004, p. 241-274.

Research output: Contribution to journalArticle

Wilson, Stephen E ; Breda D'Azevedo, Antonio. / Surfaces having no regular hypermaps. In: Discrete Mathematics. 2004 ; Vol. 277, No. 1-3. pp. 241-274.
@article{df5bf065a41847b287ef4c10afe8b38f,
title = "Surfaces having no regular hypermaps",
abstract = "The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.",
keywords = "Graphs imbeddings, Hypermaps, Maps, Non-orientable surfaces",
author = "Wilson, {Stephen E} and {Breda D'Azevedo}, Antonio",
year = "2004",
month = "2",
day = "28",
doi = "10.1016/j.disc.2003.03.001",
language = "English (US)",
volume = "277",
pages = "241--274",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Surfaces having no regular hypermaps

AU - Wilson, Stephen E

AU - Breda D'Azevedo, Antonio

PY - 2004/2/28

Y1 - 2004/2/28

N2 - The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

AB - The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic -N? We answer this question for all N from -1 to 50, and we display a body of theorems and techniques which can be used to settle the question for more complicated surfaces. These include: two ways to diagram an action of symmetry group, an equivalence relation on vertices (rotation centers in general), several applications of Sylow theory, and some non-Sylow observations on the size of the symmetry group.

KW - Graphs imbeddings

KW - Hypermaps

KW - Maps

KW - Non-orientable surfaces

UR - http://www.scopus.com/inward/record.url?scp=0742302972&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0742302972&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2003.03.001

DO - 10.1016/j.disc.2003.03.001

M3 - Article

AN - SCOPUS:0742302972

VL - 277

SP - 241

EP - 274

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -