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A Presentation for the Monoid of Uniform Block Permutations

journal contribution
posted on 2023-05-16, 14:14 authored by Desmond FitzGeraldDesmond FitzGerald
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.

History

Publication title

Bulletin of the Australian Mathematical Society

Volume

68

Pagination

317-324

ISSN

0004-9727

Department/School

School of Natural Sciences

Publisher

Australian Mathematics Publ Assoc Inc

Place of publication

Canberra, ACT, Australia

Repository Status

  • Restricted

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Expanding knowledge in the mathematical sciences

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