The topology of restricted partition posets

Abstract

For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions ${\Pi }_{\vec{c}}^{\bullet }$ 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.

22 pages, 5 figures

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