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arXiv · 2011.11714

A new formulation of the semigroup of orientation-preserving and orientation-reversing mappings

Peter M. Higgins·Alexei Vernitski
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Abstract

We characterize 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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Peter M. Higgins, Alexei Vernitski. 2020-11-23. A new formulation of the semigroup of orientation-preserving and orientation-reversing mappings. https://arxiv.org/abs/2011.11714

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