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Title:
The Topology of Restricted Partition Posets
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Abstract:
The d-divisible partition lattice is the collection of all partitions of an n-element set where each block size is divisible by d. Stanley showed that the Mobius function of the d-divisible partition lattice is given (up to a sign) by the number of permutations on n-1 elements where every dth position is a descent. Wachs showed that this lattice has an EL-shelling, and hence obtained as a corollary that the homotopy type of the order complex is a wedge of spheres. Finally, Calderbank, Hanlon and Robinson considered the action of the symmetric group on the top homology group and showed it is a Specht module of a border strip corresponding to the composition (d,...,d,d-1). Using a different proof approach, we will generalize these results to any descent pattern.
This is joint work with JiYoon Jung.
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