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

In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing ele...

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Bibliographic Details
Main Author: Fernandes, Vítor H. (author)
Other Authors: Quinteiro, Teresa (author)
Format: article
Language:eng
Published: 2015
Subjects:
Order-Preserving/Reversing
Orientation-Preserving/Reversing
Extensive
Equivalence-Preserving
Transformations
Finite Chain
Semidirect Products
Greens Relations
Semigroups
Order
Orientation
Mappings
Equivalence
Idempotent
Regularity
Online Access:http://hdl.handle.net/10400.21/5139
Country:Portugal
Oai:oai:repositorio.ipl.pt:10400.21/5139
Description
Summary:In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.

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