Filters in the partition lattice

Richard Ehrenborg, Dustin Hedmark

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Given a filter Δ in the poset of compositions of n, we form the filter in the partition lattice. We determine all the reduced homology groups of the order complex of as Sn - 1-modules in terms of the reduced homology groups of the simplicial complex Δ 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 with 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
Pages (from-to)403-439
Number of pages37
JournalJournal of Algebraic Combinatorics
Issue number3
StatePublished - May 1 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.


  • Homology
  • Partition
  • Representation theory
  • Symmetric group

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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