We study the idempotent generated subsemigroup of the partition monoid. In the finite case this subsemigroup consists of the identity and all the singular partitions. In the infinite case, the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation. As one of several corollaries, we deduce Howieʼs description from 1966 of the semigroup generated by the idempotents of a full transformation semigroup.

Item Type:	Refereed Article
Keywords:	partition monoids, transformation semigroups, symmetric inverse semigroups, dual symmetric inverse semigroups, idempotents
Research Division:	Mathematical Sciences
Research Group:	Pure Mathematics
Research Field:	Group Theory and Generalisations
Objective Division:	Expanding Knowledge
Objective Group:	Expanding Knowledge
Objective Field:	Expanding Knowledge in the Mathematical Sciences
UTAS Author:	FitzGerald, DG (Dr Des FitzGerald)
ID Code:	82416
Year Published:	2012
Web of Science® Times Cited:	18
Deposited By:	Mathematics and Physics
Deposited On:	2013-02-01
Last Modified:	2017-11-15
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