## JiYoon Jung, The topology of restricted partition posets

The topology of restricted partition posets
2014/11/04 Tuesday 4PM-5PM
Room 1409
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.

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