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)

Abstract

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
Volume131
Early online date9 Dec 2014
DOIs
Publication statusPublished - Apr 2015

Keywords

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

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