Idempotent rank in the endomorphism monoid of a non-uniform partition

Abstract

We calculate the rank and idempotent rank of the semigroup $E(X,P)$ generated by the idempotents of the semigroup $T(X,P)$, which consists of all transformations of the finite set $X$ preserving a non-uniform partition $P$. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.

12 pages; 4 figures

References in corpus (1)

• The rank of the semigroup of transformations stabilising a partition of a finite set

Cited by in corpus (4)

• Motzkin monoids and partial Brauer monoids
• Idempotent generation in the endomorphism monoid of a uniform partition
• On certain Semigroups of Transformations that preserve a partition
• Regular, Unit-regular, and Idempotent elements of semigroups of transformations that preserve a partition