TY - JOUR
T1 - Enumeration of idempotents in diagram semigroups and algebras
AU - Dolinka, Igor
AU - East, James
AU - Evangelou, Athanasios
AU - FitzGerald, Des
AU - Ham, Nicholas
AU - Hyde, James
AU - Loughlin\, Nicholas
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - algebra
KW - idempotents
KW - monoids
UR - http://hdl.handle.net/1959.7/uws:29070
U2 - 10.1016/j.jcta.2014.11.008
DO - 10.1016/j.jcta.2014.11.008
M3 - Article
SN - 0097-3165
VL - 131
SP - 119
EP - 152
JO - Journal of Combinatorial Theory, Series A
JF - Journal of Combinatorial Theory, Series A
IS - 4
ER -