Oriented transformations on a finite chain: another description

Abstract

Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in "Orientation-preserving and orientation-reversing mappings: a new description", Semigroup Forum 104 (2022), 509--514, in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.

Includes corrigendum (awaiting publication also in Commun. Korean Math. Soc.). arXiv admin note: substantial text overlap with arXiv:2205.02196