Enumeration of idempotents in diagram semigroups and algebras

Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, Nicholas Ham, James Hyde, Nicholas 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
    Issue number4
    DOIs
    Publication statusPublished - 2015

    Keywords

    • algebra
    • idempotents
    • monoids

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