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On the monoids of transformations that preserve the order and a uniform partition

TítuloOn the monoids of transformations that preserve the order and a uniform partition
Publication TypeUnpublished
Year of Publication2009
AuthorsFernandes VH, Quinteiro TM
Series TitlePreprint
AbstractIn this paper we consider the monoid $O_{m \times n}$ of all order-preserving full transformations on a chain with $mn$ elements that preserve a uniform $m$-partition and its submonoids $O_{m \times n}^+$ and $O_{m \times n}^-$ of all extensive transformations and of all co-extensive transformations, respectively. We give formulas for the number of elements of these monoids and determine their ranks. Moreover, we construct a bilateral semidirect product decomposition of $O_{m \times n}$ in terms of $O_{m \times n}^-$ and $O_{m \times n}^+$.
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2009/11_09.pdf