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

Ilinka Dimitrova; Vítor H. Fernandes; Jörg Koppitz; Teresa M. Quinteiro

doi:10.1007/s00233-023-10396-5

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

Rings and Algebras 2023-11-06 v2

Authors: Ilinka Dimitrova , Vítor H. Fernandes , Jörg Koppitz , Teresa M. Quinteiro

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Abstract

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

Keywords

dihedral inverse monoid submonoids presentations orientation-preserving transformations monotone transformations order-preserving transformations

Cite

@article{arxiv.2301.02474,
  title  = {Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set},
  author = {Ilinka Dimitrova and Vítor H. Fernandes and Jörg Koppitz and Teresa M. Quinteiro},
  journal= {arXiv preprint arXiv:2301.02474},
  year   = {2023}
}

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arXiv admin note: text overlap with arXiv:2205.02196

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

Abstract

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