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Oriented transformations on a finite chain: another description

Vítor H. Fernandes

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.

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.
Paper Structure (2 sections, 8 theorems, 5 equations)

This paper contains 2 sections, 8 theorems, 5 equations.

Table of Contents

  1. The description
  2. An application

Key Result

Proposition 1.1

Let $\alpha\in\mathcal{T}_n$. Then:

Theorems & Definitions (8)

  • Proposition 1.1
  • Corollary 1.2
  • Corollary 1.3
  • Theorem 1.4
  • Lemma 1.5
  • Theorem 1.6
  • Theorem 1.7
  • Proposition 2.1