Online Library TheLib.net » Enumeration of idempotents in diagram semigroups and algebras
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.
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