Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set

Abstract

In this paper we consider the submonoids ${\mathcal{O}\mathcal{PD}\mathcal{I}}_n$, ${\mathcal{M}\mathcal{D}\mathcal{I}}_n$ and ${\mathcal{O}\mathcal{D}\mathcal{I}}_n$ of the dihedral inverse monoid ${\mathcal{D}\mathcal{I}}_n$ of all orientation-preserving, monotone and order-preserving transformations, respectively. Our goal is to exhibit presentations for each of these three monoids.

arXiv admin note: text overlap with arXiv:2205.02196

References in corpus (2)

• On three submonoids of the dihedral inverse monoid on a finite set
• On the cyclic inverse monoid on a finite set