| Title | The cardinal of various monoids of transformations that preserve a uniform partition |
| Publication Type | Unpublished |
| Year of Publication | 2010 |
| Authors | Fernandes VH, Quinteiro TM |
| Series Title | Preprint |
| Keywords | equivalence-preserving, extensive, order-preserving/reversing, orientation-preserving/reversing, transformations |
| Abstract | In this paper we give formulas for the number of elements of the monoids ${\cal{OR}}_{m \times n}$ of all full transformations on a finite chain with $mn$ elements that preserve a uniform $m$-partition and preserve or reverse the orientation and for its submonoids ${\cal{OD}}_{m \times n}$ of all order-preserving or order-reversing elements, ${\cal{OP}}_{m\times n}$ of all orientation-preserving elements, ${\cal{O}}_{m \times n}$ of all order-preserving elements, ${\cal{O}}_{m \times n}^+$ of all extensive order-preserving elements and ${\cal{O}}_{m \times n}^-$ of all co-extensive order-preserving elements. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2010/15_10.pdf |
