| Title | On the ranks of certain monoids of transformations that preserve a uniform partition |
| Publication Type | Unpublished |
| Year of Publication | 2011 |
| Authors | Fernandes VH, Quinteiro TM |
| Series Title | Preprint |
| Keywords | equivalence-preserving transformations, order-preserving transformations, orientation-preserving transformations |
| Abstract | The purpose of this paper is to compute the ranks of the monoid ORmxn of all orientation-preserving or orientation-reversing full transformations on a chain with mn elements that preserve a uniform m-partition and of its submonoids OPmxn of all orientation-preserving transformations and ODmxn of all order-preserving or order-reversing full transformations. These three monoids are natural extensions of Omxn, the monoid of all order-preserving full transformations on a chain with mn elements that preserve a uniform m-partition. Moreover, we also determine the ranks of certain semigroups of orientation-preserving full transformations with restricted ranges. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2011/2_11.pdf |
