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A presentation for the monoid of uniform block permutations
FitzGerald, DG (2003) A presentation for the monoid of uniform block permutations. Bulletin of the Australian Mathematical Society, 68. pp. 317-324. ISSN 0004-9727
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The monoid Fn of uniform block bijections is the factorizable 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 factorizable part of the dual symmetric inverse monoid. The
present paper gives and proves correct a monoid presentation for Fn: 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 factorizable inverse
monoids, and presentations of the symmetric group and the join semilattice
of equivalences on an n-set.
|Keywords:||inverse semigroups, factorizable inverse monoids, generators and relations|
|Journal or Publication Title:||Bulletin of the Australian Mathematical Society|
|Page Range:||pp. 317-324|
Different title on PDF
This is the author's preprint version, which differs from the published version in having an older address, and omitting an introductory paragraph and a reference, added in proof, to M. Kosuda, Ryuku Math. J.13 (2000) 7-22.
|Date Deposited:||12 Sep 2007|
|Last Modified:||18 Nov 2014 03:22|
|Item Statistics:||View statistics for this item|
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