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

Producción científica: Article › revisión exhaustiva

5 Citas (SciVal)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	643-666
Número de páginas	24
Publicación	Journal of Algebraic Combinatorics
Volumen	37
N.º	4
DOI	https://doi.org/10.1007/s10801-012-0379-8
Estado	Published - jun 2013

Nota bibliográfica

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.

Financiación

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.

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	0835373, 0902063, DMS-0902063, 0832797
Institute for Advanced Study	CCF-0832797, DMS-0835373

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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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.",

keywords = "Border strip Specht module, Complex of ordered set partitions, Descent set statistics, Knapsack integer partitions, Poset of pointed set partitions",

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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.

KW - Border strip Specht module

KW - Complex of ordered set partitions

KW - Descent set statistics

KW - Knapsack integer partitions

KW - Poset of pointed set partitions

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The topology of restricted partition posets

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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