Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups

The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation groups (those which act transitively on the subsets of size k of their domain X) where \vert X\vert=n and k