The topology of restricted partition posets

Richard Ehrenborg; Ji Yoon Jung

doi:10.1007/s10801-012-0379-8

The topology of restricted partition posets

Richard Ehrenborg
, Ji Yoon Jung

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (SciVal)

Abstract

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 S^B 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.

Original language	English
Pages (from-to)	643-666
Number of pages	24
Journal	Journal of Algebraic Combinatorics
Volume	37
Issue number	4
DOIs	https://doi.org/10.1007/s10801-012-0379-8
State	Published - Jun 2013

Bibliographical note

Funding 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.

Funding

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.

Funders	Funder number
National Science Foundation Arctic Social Science Program	0835373, 0902063, DMS-0902063, 0832797
Institute for Advanced Study	CCF-0832797, DMS-0835373

Keywords

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

Access to Document

10.1007/s10801-012-0379-8

Cite this

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abstract = "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.",

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N2 - 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.

AB - 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.

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KW - Complex of ordered set partitions

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KW - Knapsack integer partitions

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The topology of restricted partition posets

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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