31 citations · 211 across the 34 of their papers we have counts for
6 papers · 1 filter
Variants of finite full transformation semigroups
Igor Dolinka, James East
The variant of a semigroup S with respect to an element a in S, denoted S^a, is the semigroup with underlying set S and operation * defined by x*y=xay for x,y in S. In this article…
Enumeration of idempotents in diagram semigroups and algebras
Igor Dolinka, James East, Athanasios Evangelou +4
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…
Idempotent generation in the endomorphism monoid of a uniform partition
Igor Dolinka, James East
Denote by and the full transformation semigroup and the symmetric group on the set , and $\mathcal E_n=\{1\}\cup(\mathcal T_n\setminus…
Infinite partition monoids
James East
Let and be the partition monoid and symmetric group on an infinite set . We show that may be generated by together wi…
Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals
James East, Robert Gray
We study the ideals of the partition, Brauer, and Jones monoid, establishing various combinatorial results on generating sets and idempotent generating sets via an analysis of thei…
Enumerating Transformation Semigroups
James East, Attila Egri-Nagy, James D. Mitchell
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application…