On the poset of weighted partitions

Rafael S.González D'León, Michelle L. Wachs

Research output: Contribution to journalConference articlepeer-review


In this extended abstract we consider the poset of weighted partitions ∏wn , introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of ∏wn provide a generalization of the lattice ∏n of partitions, which we show possesses many of the well-known properties of ∏n. In particular, we prove these intervals are EL-shellable, we compute the M̈obius invariant in terms of rooted trees, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted On-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 ∏wnhas a nice factorization analogous to that of ∏n.

Original languageEnglish (US)
Pages (from-to)1029-1040
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - Nov 18 2013
Event25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France
Duration: Jun 24 2013Jun 28 2013


  • Free lie algebra
  • Partitions
  • Poset topology
  • Rooted trees

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics


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