## Richard Ehrenborg ; JiYoon Jung - The topology of restricted partition posets

dmtcs:2910 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2910
The topology of restricted partition posets

Authors: Richard Ehrenborg ; JiYoon Jung

For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $Π ^• _{\vec{c}}$ is a wedge of $β\vec{c}$ spheres of the same dimensions, where $β\vec{c}$ is 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 $\vec{c}$. 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.

Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Pointed set partitions,descent set statistics,top homology group,Specht module,knapsack partitions.,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Fundings :
Source : OpenAIRE Research Graph
• Bruhat and balanced graphs, manifolds, partitions and affine permutations; Funder: National Science Foundation; Code: 0902063
• CDI Type II: Pseudorandomness; Funder: National Science Foundation; Code: 0835373
• Collaborative Research: Understanding, Coping with, and Benefiting from Intractibility.; Funder: National Science Foundation; Code: 0832797