Generating Sets of Finite Transformation Semigroups PK(n, r) and K (n, r)

Let Pn and Tn be the partial transformation and the full transformation semigroups on the set {1,…, n}, respectively. In this paper we find necessary and sufficient conditions for any set of partial transformations of height r in the subsemigroup PK(n, r) = {? ?Pn: |im (?)| ?r} of Pn to be a (minimal) generating set of PK(n, r); and similarly, for any set of full transformations of height r in the subsemigroup K(n, r) = {? ?Tn: |im (?)| ?r} of Tn to be a (minimal) generating set of K(n, r) for 2 ? r ? n - 1. © 2015 Taylor & Francis Group, LLC