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A Presentation for the Monoid of Uniform Block Permutations
journal contributionposted 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.
Publication titleBulletin of the Australian Mathematical Society
Department/SchoolSchool of Natural Sciences
PublisherAustralian Mathematics Publ Assoc Inc
Place of publicationCanberra, ACT, Australia