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arXiv · 1312.2036

The topology of restricted partition posets

Richard Ehrenborg·JiYoon Jung
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Abstract

For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $Π^{\bullet}_{\vec{c}}$ 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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Richard Ehrenborg, JiYoon Jung. 2013-12-06. The topology of restricted partition posets. https://doi.org/10.1007/s10801-012-0379-8

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