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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, N
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.

History

Publication title

Journal of Combinatorial Theory, Series A

Volume

131

Pagination

119-152

ISSN

0097-3165

Department/School

School of Natural Sciences

Publisher

Academic Press Inc Elsevier Science

Place of publication

525 B St, Ste 1900, San Diego, USA, Ca, 92101-4495

Rights statement

Copyright 2015 Elsevier

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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