On factorisations and generators in transformation semigroups.
type: Item
instance of: scholarly article
title: On factorisations and generators in transformation semigroups.
zbMATH Open document ID: 1072.20078
author: Gonca Ayık
author: Hayrullah Ayık
author: John M. Howie
published in: Semigroup Forum
publication date: 2005-06-06T00:00:00Z
review text: A cycle-style notation is introduced for members of the full transformation semigroup similar to that used by Lipscomb for partial one-to-one maps. This approach is used to study generating sets of the submonoids \(T_{n,r}\) of \(T_n\) consisting of the union of the symmetric group and the ideal of all mappings with range of cardinality no greater than \(r\) (\(\leq n\)). The least number of singular elements in any generating set for \(T_{n,r}\) is the number of partitions of \(n\) with \(r\) terms.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 2173797
zbMATH Keywords: transformation semigroups
zbMATH Keywords: numbers of partitions
zbMATH Keywords: singular mappings
zbMATH Keywords: generating sets
MaRDI profile type: Publication
full work available at URL: s00233-004-0145-x
OpenAlex ID: W1995666405
DOI: 10.1007/S00233-004-0145-X
description: scientific article; zbMATH DE number 2173797