Orientation-preserving and orientation-reversing mappings: a new description
Combinatorics
2022-01-19 v1
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.
Cite
@article{arxiv.2201.05879,
title = {Orientation-preserving and orientation-reversing mappings: a new description},
author = {Peter M. Higgins and Alexei Vernitski},
journal= {arXiv preprint arXiv:2201.05879},
year = {2022}
}
Comments
5 pages, 1 figure