# School of Computing, Engineering and Mathematics Seminars

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## Idempotent generators in partition monoids

Speaker: James East

Affiliation: University of Western Sydney

Time: Monday 08/07/2013 from 14:00 to 15:00

Venue: Access Grid UWS. Presented from Parramatta (EB.1.32), accessible from Campbelltown (26.1.50) and Penrith (Y239).

Abstract: Denote by $T_n$ and $S_n$ the full transformation semigroup and the symmetric group on the finite set $\{1,\ldots,n\}$. In 1966, John Howie showed that $T_n\setminus S_n$, the so-called singular part of $T_n$, is generated by its idempotents. Subsequent work by Howie and others calculated the number of minimal idempotent generating sets for $T_n\setminus S_n$ and also the rank and idempotent rank of other ideals of $T_n$. In this talk, I'll outline the corresponding results for the partition monoid and some of its submonoids, including the Brauer and Jones monoids. This is joint work with Bob Gray (University of East Anglia).

Biography: James is a member of the Centre for Research in Mathematics and a lecturer with the School of Computing, Engineering and Mathematics.

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