%0 Journal Article %T Idempotent rank in the endomorphism monoid of a non-uniform partition %A Igor Dolinka %A James East %A James D. Mitchell %J Mathematics %D 2015 %I arXiv %X 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. %U http://arxiv.org/abs/1504.02520v1