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 language | English |
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Pages (from-to) | 119-152 |
Number of pages | 34 |
Journal | Journal of Combinatorial Theory, Series A |
Volume | 131 |
Early online date | 9 Dec 2014 |
DOIs | |
Publication status | Published - Apr 2015 |
Keywords
- Partition monoids
- Partition algebras
- Brauer monoids
- Brauer algebras idempotents
- Enumeration