Filters in the partition lattice

Richard Ehrenborg, Dustin Hedmark

Research output: Contribution to conferencePaperpeer-review

Abstract

Given a filter Λ in the poset of compositions of n, we form the filter ΠΔin the partition lattice. We determine all the reduced homology groups of the order complex of ΠΔas Sn-1-modules in terms of the reduced homology groups of the simplicial complex A and in terms of Specht modules of border shapes. We also obtain the homotopy type of this order complex. These results generalize work of Calderbank-Hanlon-Robinson and Wachs on the d-divisible partition lattice. Our main theorem applies to a plethora of examples, including filters associated to integer knapsack partitions and filters generated by all partitions having block sizes a or b. We also obtain the reduced homology groups of the filter generated by all partitions having block sizes belonging to the arithmetic progression a, a + d,⋯,a + (a - 1) • d, extending work of Browdy.

Original languageEnglish
StatePublished - 2006
Event29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom
Duration: Jul 9 2017Jul 13 2017

Conference

Conference29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/TerritoryUnited Kingdom
CityLondon
Period7/9/177/13/17

Bibliographical note

Funding Information:
The authors thank Bert Guillou and Kate Ponto for their homological guidance and expertise. They also thank Sheila Sundaram and Michelle Wachs for essential references. The authors thank Margaret Readdy for her comments on an earlier draft. Both authors were partially supported by National Security Agency grant H98230-13-1-0280. The first author wishes to thank the Princeton University Mathematics Department where this work began.

Publisher Copyright:
© 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Keywords

  • Composition lattice
  • Equivariant Quillen's Fiber Lemma
  • Frobenius complex
  • Partition lattice
  • Specht module

ASJC Scopus subject areas

  • Algebra and Number Theory

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