Regular self-dual and self-Petrie-dual maps of arbitrary valency - Fraser, Jay (Ars mathematica contemporanea, 2019)
The existence of a regular, self-dual and self-Petrie-dual map of any given even valency has been proved by D. Archdeacon et al. Trans. Am. Math. Soc. 366, No. 8, 4491--4512 (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.
Keywords: automorphism group; grupa avtomorfizmov; regular map; regularni zemljevid; sebi-dualen zemljevid; sebi-Petriejevo-dualen zemljevid; self-dual map; self-Petrie-dual map