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

2023/01/04 by Dimitrova, Ilinka, Fernandes, Vítor H., Koppitz, Jörg +1
#05C12 #05C25 #20M10 #20M20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2301.01519

Abstract

In this paper we consider three submonoids of the dihedral inverse monoid DI_n, namely its submonoids OPDI_n, MDI_n and 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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