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A presentation for the monoid of uniform block permutations

Published online by Cambridge University Press:  17 April 2009

D. G. FitzGerald
D. G. FitzGerald
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tas 7001 Australia, e-mail: D.FitzGerald@utas.edu.au
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Abstract

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The monoid n 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n. 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 317 - 324
Copyright
Copyright © Australian Mathematical Society 2003

References

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