GENERATING SETS OF STRICTLY ORDER-PRESERVING TRANSFORMATION SEMIGROUPS ON A FINITE SET

Let O-n and POn, denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set X-n = {1,...,n}, respectively. Then the strictly partial order-preserving transformation semigroup SPOn on the set X-n, under its natural or der, is defined by SPOn = POn\O-n In this paper we find necessary and sufficient conditions for any subset of SPO(n,r) to be a (minimal) generating set of SPO(n,r) for 2 <= r <= n - 1.