The topology of restricted partition posets

JiYoon Jung

NIMS

NIMS

2014/11/04 Tuesday 4PM-5PM

Room 1409

Room 1409

For each composition we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition . Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module where 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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