English

Regular self-dual and self-Petrie-dual maps of arbitrary valency

Combinatorics 2018-08-01 v1

Abstract

The main result of D. Archdeacon, M. Conder and J. \v{S}ir\'a\v{n} [Trans. Amer. Math. Soc. 366 (2014) 8, 4491-4512] implies existence of a regular, self-dual and self-Petrie dual map of any given even valency. In this paper we extend this result to any odd valency 5\ge 5. This is done by algebraic number theory and maps defined on the groups PSL(2,p){\rm PSL}(2,p) in the case of odd prime valency 5\ge 5 and valency 99, and by coverings for the remaining odd valencies.

Keywords

Cite

@article{arxiv.1807.11692,
  title  = {Regular self-dual and self-Petrie-dual maps of arbitrary valency},
  author = {Jay Fraser and Olivia Jeans and Jozef Širáň},
  journal= {arXiv preprint arXiv:1807.11692},
  year   = {2018}
}