THE HOMOLOGY REPRESENTATIONS OF THE K-EQUAL PARTITION LATTICE

We determine the character of the action of the symmetric group on the homology of the induced subposet of the lattice of partitions of the set {1, 2,...,n} obtained by restricting block sizes to the set {1, k, k + 1,...}. A plethystic formula for the generating function of the F robenius characteristic of the representation is given. We combine tec hniques from the theory of nonpure shellability, recently developed by Bjorner and Wachs, with symmetric function techniques, developed by S undaram, for determining representations on the homology of subposets of the partition lattice.