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A Presentation for the Monoid of Uniform Block Permutations

Citation

FitzGerald, DG, A Presentation for the Monoid of Uniform Block Permutations, Bulletin of the Australian Mathematical Society, 68, (2) pp. 317-324. ISSN 0004-9727 (2003) [Refereed Article]

DOI: doi:10.1017/S0004972700037692

Abstract

The monoid script f signn of uniform block permutations is the factorisable inverse monoid which arises from the natural action of the symmetric group on the join semilattice of equivalences on an n-set; it has been described in the literature as the factorisable part of the dual symmetric inverse monoid. The present paper gives and proves correct a monoid presentation for script f signn. The methods involved make use of a general criterion for a monoid generated by a group and an idempotent to be inverse, the structure of factorisable inverse monoids, and presentations of the symmetric group and the join semilattice of equivalences on an n-set.

Item Details

Item Type:Refereed Article
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
Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:27022
Year Published:2003
Web of Science® Times Cited:19
Deposited By:Mathematics
Deposited On:2003-08-01
Last Modified:2007-10-12
Downloads:0

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