Richter, Bruce R.; Siran, Jozef and Wang, Yan
(2012).
| DOI (Digital Object Identifier) Link: | http://dx.doi.org/doi:10.1002/jgt.20570 |
|---|---|
| Google Scholar: | Look up in Google Scholar |
Abstract
Regular maps are cellular decompositions of surfaces with the “highest level of symmetry”, not necessarily orientation-preserving. Such maps can be identified with three-generator presentations of groups G of the form G=‹a,b,c|a2 =b2=c2=(ab)k =(bc)m=(ca)2 =•••=1›; the positive integers k and m are the face length and the vertex degree of the map. A regular map (G;a,b,c) is self-dual if the assignment b|→b,c |→a and a |→c extends to an automorphism of G, and self-Petrie-dual if G admits an automorphism fixing b and c and interchanging a with ca. In this note we show that for infinitely many numbers k there exist finite, self-dual and self-Petrie-dual regular maps of vertex degree and face length equal to k. We also prove that no such map with odd vertex degree is a normal Cayley map.
| Item Type: | Journal Article |
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| Copyright Holders: | 2011 Wiley Periodicals, Inc |
| ISSN: | 0364-9024 |
| Funders: | NSERC, VEGA Research Grant [1/0489/08], APVV Research Grant [0040-06 and 0104-07], APVV LPP Research Grant [0145-06 and 0203-06] |
| Keywords: | regular map; triangle group; self-dual map; self-Petrie-dual map |
| Academic Unit/Department: | Mathematics, Computing and Technology Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: | 32160 |
| Depositing User: | Jozef Siran |
| Date Deposited: | 03 Feb 2012 11:54 |
| Last Modified: | 30 Nov 2012 10:40 |
| URI: | http://oro.open.ac.uk/id/eprint/32160 |
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