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Richter, Bruce R.; Siran, Jozef and Wang, Yan
(2012).
DOI: https://doi.org/10.1002/jgt.20570
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.
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About
- Item ORO ID
- 32160
- Item Type
- Journal Item
- ISSN
- 0364-9024
- Project Funding Details
-
Funded Project Name Project ID Funding Body Not Set Not Set NSERC Not Set Not Set VEGA Research Grant [1/0489/08] Not Set Not Set APVV Research Grant [0040-06 and 0104-07] Not Set Not Set APVV LPP Research Grant [0145-06 and 0203-06] - Keywords
- regular map; triangle group; self-dual map; self-Petrie-dual map
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics - Copyright Holders
- © 2011 Wiley Periodicals, Inc
- Depositing User
- Jozef Širáň