Rafael González S. D'León ; Michelle L. Wachs - Weighted partitions

dmtcs:2363 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2363
Weighted partitionsArticle

Authors: Rafael González S. D'León ; Michelle L. Wachs 1

  • 1 Department of Mathematics [Miami]

In this extended abstract we consider the poset of weighted partitions Π _n^w, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of Π _n^w provide a generalization of the lattice Π _n of partitions, which we show possesses many of the well-known properties of Π _n. In particular, we prove these intervals are EL-shellable, we compute the Möbius invariant in terms of rooted trees, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted <mathfrak>S</mathfrak>_n-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 Π _n^w has a nice factorization analogous to that of Π _n.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: poset topology,partitions,free Lie algebra,rooted trees,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Research in Algebraic Combinatorics; Funder: National Science Foundation; Code: 0902323
  • Research in Algebraic Combinatorics; Funder: National Science Foundation; Code: 1202755

Consultation statistics

This page has been seen 283 times.
This article's PDF has been downloaded 742 times.