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

2020/11/23 by Peter M. Higgins, Higgins, Peter M., Alexei Vernitski +1
Computer Science · Mathematics · #20M20 #FOS: Mathematics #Finite Group Theory Research #Functional Equations Stability Results #Geometric and Algebraic Topology #Group Theory (math.GR) #Matrix Theory and Algorithms #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2011.11714

openalex publication_date 2020/11/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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

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