## Abstract Regular maps are cellular decompositions of surfaces with the βhighest level of symmetryβ, not necessarily orientationβpreserving. Such maps can be identified with threeβgenerator presentations of groups __G__ of the form __G__ = γ__a, b, c__|__a__^2^ = __b__^2^ = __c__^2^ = (__ab__)^__
Self-dual Cayley Maps
β Scribed by Mark S. Anderson; R. Bruce Richter
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 136 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0195-6698
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β¦ Synopsis
The purpose of this paper is to study self-dual embeddings of balanced Cayley maps. Given a Cayley map, necessary and sufficient conditions are given in terms of its underlying group for the map to be isomorphic to its dual embedding. Applications include self-dual embeddings of 2n-dimensional cubes.
π SIMILAR VOLUMES
Let 1 be a finite group and let 2 be a generating set for 1. A Cayley map associated with 1 and 2 is an orientable 2-cell imbedding of the Cayley graph G 2 (1 ) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A
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In this note, the existence of self-dual codes and formally self-dual even codes is investigated. A construction for self-dual codes is presented, based on extending generator matrices. Using this method, a singly-even self-dual [70, 35, code is constructed from a self-dual code of length 68. This i