Abstract
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 forn. 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.
Publisher
Cambridge University Press (CUP)
Reference6 articles.
1. Defining relations in some semigroups of partial transformations of a finite set;Popova;Uchenye Zap. Leningrad. Gos. Ped. Inst.,1961
2. Concerning the abstract groups of order k! and ½k! holohedrically isomorphic with the symmetric and alternating substitution groups on k letters;Moore;Proc. London Math. Soc.,1897
3. Inverse Semigroups
4. Dual symmetric inverse monoids and representation theory
5. Factorizable inverse semigroups
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