On the (CO)homology of the poset of weighted partitions

Rafael S. González D’león, Michelle L. Wachs

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6 Scopus citations


We consider the poset of weighted partitions Πwn, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of Πwn provide a generalization of the lattice Πn of partitions, which we show possesses many of the well-known properties of Πn. In particular, we prove these intervals are EL-shellable, we show that the bius invariant of each maximal interval is given up to sign by the number of rooted trees on node set {1, 2,…, n} having a fixed number of descents, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted Sn-module isomorphism from cohomology to the multilinear component of the free Lie algebra with two compatible brackets. We also show that the characteristic polynomial of Πwn has a nice factorization analogous to that of Πn.

Original languageEnglish (US)
Pages (from-to)6779-6818
Number of pages40
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - Oct 1 2016

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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