Geodesic
The topology of restricted partition posets
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 4, pp. 643-666.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: border strip Specht module, complex of ordered set partitions, descent set statistics, knapsack integer partitions, poset of pointed set partitions 
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     author = {Ehrenborg, Richard and Jung, JiYoon},
     title = {The topology of restricted partition posets},
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Ehrenborg, Richard; Jung, JiYoon. The topology of restricted partition posets. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 4, pp. 643-666. http://geodesic.mathdoc.fr/item/JAC_2013__37_4_a6/