The topology of restricted partition posets |
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Authors: | Richard Ehrenborg JiYoon Jung |
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Affiliation: | 1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA
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Abstract: | 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. |
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