The topology of restricted partition posets
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...
Published in: | Discrete Mathematics & Theoretical Computer Science |
---|---|
Main Authors: | , |
Other Authors: | , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2011
|
Subjects: | |
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 |
id |
ftccsdartic:oai:HAL:hal-01215111v1 |
---|---|
record_format |
openpolar |
spelling |
ftccsdartic:oai:HAL:hal-01215111v1 2023-05-15T16:51:23+02:00 The topology of restricted partition posets Ehrenborg, Richard Jung, Jiyoon Department of Mathematics (Kentucky) University of Kentucky (UK) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 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 en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2910 hal-01215111 https://hal.inria.fr/hal-01215111 https://hal.inria.fr/hal-01215111/document https://hal.inria.fr/hal-01215111/file/dmAO0126.pdf doi:10.46298/dmtcs.2910 info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215111 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.281-292, ⟨10.46298/dmtcs.2910⟩ 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] info:eu-repo/semantics/conferenceObject Conference papers 2011 ftccsdartic https://doi.org/10.46298/dmtcs.2910 2023-03-05T11:38:04Z 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 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. Pour chaque composition $\vec{c}$ nous montrons que le complexe simplicial des chaînes de l'ensemble ordonné $Π ^• _{\vec{c}}$ des partitions pointées d'un ensemble est un bouquet de $β\vec{c}$ sphères de même dimension, où $β\vec{c}$ est le nombre de permutations ayant la composition de descentes $\vec{c}$. De plus, l'action du groupe symétrique sur le groupe d'homologie de degré maximum est isomorphe au module de Specht $S^B$ où $B$ est la bande frontalière associée à la composition $\vec{c}$. Nous étudions aussi le filtre des partitions pointées d'un ensemble, engendré par des partitions d'entiers de type "sac à dos'' et nous démontrons des résultats analogues pour le type d'homotopie et pour l'action sur le groupe d'homologie de degré maximum. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Bouquet ENVELOPE(-62.166,-62.166,-64.050,-64.050) Discrete Mathematics & Theoretical Computer Science DMTCS Proceeding Proceedings |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
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] |
spellingShingle |
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] Ehrenborg, Richard Jung, Jiyoon The topology of restricted partition posets |
topic_facet |
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] |
description |
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 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. Pour chaque composition $\vec{c}$ nous montrons que le complexe simplicial des chaînes de l'ensemble ordonné $Π ^• _{\vec{c}}$ des partitions pointées d'un ensemble est un bouquet de $β\vec{c}$ sphères de même dimension, où $β\vec{c}$ est le nombre de permutations ayant la composition de descentes $\vec{c}$. De plus, l'action du groupe symétrique sur le groupe d'homologie de degré maximum est isomorphe au module de Specht $S^B$ où $B$ est la bande frontalière associée à la composition $\vec{c}$. Nous étudions aussi le filtre des partitions pointées d'un ensemble, engendré par des partitions d'entiers de type "sac à dos'' et nous démontrons des résultats analogues pour le type d'homotopie et pour l'action sur le groupe d'homologie de degré maximum. |
author2 |
Department of Mathematics (Kentucky) University of Kentucky (UK) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Ehrenborg, Richard Jung, Jiyoon |
author_facet |
Ehrenborg, Richard Jung, Jiyoon |
author_sort |
Ehrenborg, Richard |
title |
The topology of restricted partition posets |
title_short |
The topology of restricted partition posets |
title_full |
The topology of restricted partition posets |
title_fullStr |
The topology of restricted partition posets |
title_full_unstemmed |
The topology of restricted partition posets |
title_sort |
topology of restricted partition posets |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
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 |
op_coverage |
Reykjavik, Iceland |
long_lat |
ENVELOPE(-62.166,-62.166,-64.050,-64.050) |
geographic |
Bouquet |
geographic_facet |
Bouquet |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215111 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.281-292, ⟨10.46298/dmtcs.2910⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2910 hal-01215111 https://hal.inria.fr/hal-01215111 https://hal.inria.fr/hal-01215111/document https://hal.inria.fr/hal-01215111/file/dmAO0126.pdf doi:10.46298/dmtcs.2910 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.46298/dmtcs.2910 |
container_title |
Discrete Mathematics & Theoretical Computer Science |
container_volume |
DMTCS Proceeding |
container_issue |
Proceedings |
_version_ |
1766041495541907456 |