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

Fraser, Jay; Jeans, Olivia and Širáň, Jozef (2019). Regular self-dual and self-Petrie-dual maps of arbitrary valency. Ars Mathematica Contemporanea, 16(2) pp. 403–410.

DOI: https://doi.org/10.26493/1855-3974.1749.84e

Abstract

The existence of a regular, self-dual and self-Petrie-dual map of any given even valency has been proved by D. Archdeacon, M. Conder and J. Siran (2014). In this paper we extend this result to any odd valency ≥ 5. This is done using algebraic number theory and maps defined on the groups PSL(2, p) in the case of odd prime valency ≥ 5 and valency 9, and using coverings for the remaining odd valencies.

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