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Enumeration of idempotents in diagram semigroups and algebras
journal contribution
posted on 2023-05-18, 08:08 authored by Dolinka, I, East, J, Evangelou, A, Desmond FitzGeraldDesmond FitzGerald, Ham, N, Hyde, J, Loughlin, NWe give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions for the number of idempotents in each monoid as well as various R-, L- and D-classes. We also apply our results to determine the number of idempotent basis elements in the finite dimensional partition, Brauer and partial Brauer algebras.
History
Publication title
Journal of Combinatorial Theory, Series AVolume
131Pagination
119-152ISSN
0097-3165Department/School
School of Natural SciencesPublisher
Academic Press Inc Elsevier SciencePlace of publication
525 B St, Ste 1900, San Diego, USA, Ca, 92101-4495Rights statement
Copyright 2015 ElsevierRepository Status
- Restricted