- Citation:
- Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "On three submonoids of the dihedral inverse monoid on a finite set." Bulletin of the Malaysian Mathematical Sciences Society (DOI 10.1007/s40840-023-01620-0; Online 11 Dec 2023). 47 (2024): 27.

### 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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