For each composition c we show that the order complex of the poset of pointed set partitions Π•c is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module SB 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.
|Number of pages||24|
|Journal||Journal of Algebraic Combinatorics|
|State||Published - Jun 2013|
Bibliographical noteFunding Information:
Acknowledgements The authors thank Serge Ochanine for many helpful discussions and Margaret Readdy, Michelle Wachs and the two referees for their comments on an earlier draft of this paper. Both authors are partially supported by National Science Foundation grant DMS-0902063. The first author also thanks the Institute for Advanced Study and is also partially supported by National Science Foundation grants DMS-0835373 and CCF-0832797.
- Border strip Specht module
- Complex of ordered set partitions
- Descent set statistics
- Knapsack integer partitions
- Poset of pointed set partitions
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics