English

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.

Keywords

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

R2 v1 2026-06-24T08:51:08.300Z