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Chiral maps of given hyperbolic type

Conder, Marston D. E.; Hucíková, Veronika; Nedela, Roman and Širáň, Jozef (2016). Chiral maps of given hyperbolic type. Bulletin of the London Mathematical Society, 48(1) pp. 38–52.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1112/blms/bdv086
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Abstract

We prove the existence of infinitely many orientably-regular but chiral maps of every given hyperbolic type {m, k}, by constructing base examples from suitable permutation representations of the ordinary (2, k, m) triangle group, and then taking abelian p-covers. The base examples also help to prove that for every pair (k, m) of integers with 1/k + 1/m ≤ 1/2, there exist infinitely many regular and infinitely many orientably-regular but chiral maps of type {m, k}, each with the property that both the map and its dual have simple underlying graph.

Item Type: Journal Item
Copyright Holders: 2015 London Mathematical Society
ISSN: 1469-2120
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 48784
Depositing User: Jozef Širáň
Date Deposited: 01 Mar 2017 16:41
Last Modified: 07 Jul 2020 07:30
URI: http://oro.open.ac.uk/id/eprint/48784
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