The homology representations of the k-equal partition lattice

Sheila Sundaram, Michelle Wachs

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We determine the character of the action of the symmetric group on the homology of the induced subposet of the lattice of partitions of the set {1,2,... ,n} obtained by restricting block sizes to the set {l, k, k + 1,... }. A plethystic formula for the generating function of the Frobenius characteristic of the representation is given. We combine techniques from the theory of nonpure shellability, recently developed by Björner and Wachs, with symmetric function techniques, developed by Sundaram, for determining representations on the homology of subposets of the partition lattice.

Original languageEnglish (US)
Pages (from-to)935-954
Number of pages20
JournalTransactions of the American Mathematical Society
Volume349
Issue number3
DOIs
StatePublished - 1997

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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