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07 February 2025

» arxiv » 2301.01519

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On three remarkable submonoids of the dihedral inverse monoid on a finite set
Ilinka Dimitrova ; Vítor H. Fernandes ; Jörg Koppitz ; Teresa M. Quinteiro ;
Date:	4 Jan 2023
Abstract:	In this paper we consider three notable 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.
Source:	arXiv, 2301.01519
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