Faculdade

Investigação

The cardinal of various monoids of transformations that preserve a uniform partition

TítuloThe cardinal of various monoids of transformations that preserve a uniform partition
Publication TypeUnpublished
Year of Publication2010
AuthorsFernandes VH, Quinteiro TM
Series TitlePreprint
Palavras-chaveequivalence-preserving, extensive, order-preserving/reversing, orientation-preserving/reversing, transformations
AbstractIn 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.
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2010/15_10.pdf