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arXiv · 2301.01519

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

Ilinka Dimitrova·Vítor H. Fernandes·Jörg Koppitz·Teresa M. Quinteiro
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Abstract

In this paper we consider three submonoids of the dihedral inverse monoid $\mathcal{DI}_n$, namely its submonoids $\mathcal{OPDI}_n$, $\mathcal{MDI}_n$ and $\mathcal{ODI}_n$ of all orientation-preserving, monotone and order-preserving transformations, respectively. For each of these three monoids, we compute the cardinal, give descriptions of Green's relations and determine the rank.

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Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro. 2023-01-04. On three submonoids of the dihedral inverse monoid on a finite set. https://arxiv.org/abs/2301.01519

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