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A Presentation for the Monoid of Uniform Block Permutations
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 SocietyVolume
68Pagination
317-324ISSN
0004-9727Department/School
School of Natural SciencesPublisher
Australian Mathematics Publ Assoc IncPlace of publication
Canberra, ACT, AustraliaRepository Status
- Restricted