The topology of restricted partition posets

• Published in: Discrete Mathematics & Theoretical Computer Science
• Main Authors: Ehrenborg, Richard, Jung, Jiyoon
• Other Authors: Department of Mathematics (Kentucky), University of Kentucky (UK), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: 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]; Bouquet; Iceland
• Online Access: https://hal.inria.fr/hal-01215111; https://hal.inria.fr/hal-01215111/document; https://hal.inria.fr/hal-01215111/file/dmAO0126.pdf; https://doi.org/10.46298/dmtcs.2910

International audience 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...