Enumeration of idempotents in diagram semigroups and algebras

I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, J. Hyde, N. Loughlin

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


We 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.
Original languageEnglish
Pages (from-to)119-152
Number of pages34
JournalJournal of Combinatorial Theory, Series A
Early online date9 Dec 2014
Publication statusPublished - Apr 2015


  • Partition monoids
  • Partition algebras
  • Brauer monoids
  • Brauer algebras idempotents
  • Enumeration


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