The topology of restricted partition posets

For each composition $\vec {c}$ we show that the order complex of the poset of pointed set partitions  $\varPi^{\bullet}_{\vec {c}}$ is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition $\vec {c}$ . Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module S ^B where B is a border strip associated to the composition. We also study the filter of pointed set partitions generated by a knapsack integer partition and show the analogous results on homotopy type and action on the top homology.