Abstract
For each composition c→ we show that the order complex of the poset of pointed set partitions π c→ • is a wedge of β(c→) spheres of the same dimensions, where β(c→) is 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 S B where B is a border strip associated to the composition c→. We also study the filter of pointed set partitions generated by a knapsack integer partitions and show the analogous results on homotopy type and action on the top homology.
| Original language | English |
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| Pages | 281-292 |
| Number of pages | 12 |
| State | Published - 2011 |
| Event | 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 - Reykjavik, Iceland Duration: Jun 13 2011 → Jun 17 2011 |
Conference
| Conference | 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 |
|---|---|
| Country/Territory | Iceland |
| City | Reykjavik |
| Period | 6/13/11 → 6/17/11 |
Keywords
- Descent set statistics
- Knapsack partitions
- Pointed set partitions
- Specht module
- Top homology group
ASJC Scopus subject areas
- Algebra and Number Theory