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

2022/01/15 by Peter M. Higgins, Higgins, Peter M., Alexei Vernitski +1 · 1 citation
Computer Science · Mathematics · #20M20 #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2201.05879

openalex publication_date 2022/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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