The semigroup generated by the idempotents of a partition monoid

We study the idempotent generated subsemigroup of the partition monoid. In the finite case this subsemigroup consists of the identity and all the singular partitions. In the infinite case, the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation. As one of several corollaries, we deduce Howieʼs description from 1966 of the semigroup generated by the idempotents of a full transformation semigroup.