A presentation for the monoid of uniform block permutations

By Dominic A. Fitzgerald. Bulletin of the Australian Mathematical Society, 2003

61 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Language and Linguistics

View Paper: https://www.semanticscholar.org/paper/28c2cdf416da9d478cb87249e88cbc0b24123103

Citations in the corpus

• On presentations of Brauer-type monoids (2005, unknown): “We thank Victor Maltcev for informing us about the reference [7].”