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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.

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DOI (Digital Object Identifier) Link: https://doi.org/10.26493/1855-3974.1749.84e
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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.

Item Type: Journal Item
ISSN: 1855-3966
Keywords: Regular map; automorphism group; self-dual map; self-Petrie-dual map.
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 60896
Depositing User: ORO Import
Date Deposited: 03 May 2019 08:06
Last Modified: 11 May 2019 17:21
URI: http://oro.open.ac.uk/id/eprint/60896
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