For each composition ~c we show that the order complex of the poset of pointed set partitions Π• ~c is a wedge of β(~c) spheres of the same dimensions, where β(~c) is the number of permutations with descent composition ~c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module S where B is a border strip associated to the composition ~c. We also study the filter of pointed set partitions generated by a knapsack integer partitions and show the… CONTINUE READING