On the poset of weighted partitions

Rafael S González D'León, Michelle L Galloway

Research output: Contribution to journalArticle

Abstract

In this extended abstract we consider the poset of weighted partitions ∏w n , introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of ∏w n 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 ∏w nhas 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 - 2013

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Factorization
Poset
Algebra
Cohomology
Partition
Polynomials
Free Lie Algebra
Operad
Interval
Möbius
Rooted Trees
Characteristic polynomial
Brackets
Homology
Isomorphism
Module
Invariant
Generalization

Keywords

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

ASJC Scopus subject areas

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

Cite this

On the poset of weighted partitions. / D'León, Rafael S González; Galloway, Michelle L.

In: Discrete Mathematics and Theoretical Computer Science, 2013, p. 1029-1040.

Research output: Contribution to journalArticle

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