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Orientation-preserving and orientation-reversing mappings: a new description

Higgins, Peter and Vernitski, Alexei (2022) 'Orientation-preserving and orientation-reversing mappings: a new description.' Semigroup Forum, 104 (2). pp. 509-514. ISSN 0037-1912

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Abstract

We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter semigroup coincides with the semigroup of all mappings that preserve intersections of chords on the corresponding circle.

Item Type: Article
Uncontrolled Keywords: orientation-preserving; transformation semigroup
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 25 Feb 2022 10:46
Last Modified: 06 May 2022 09:47
URI: http://repository.essex.ac.uk/id/eprint/32060

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