Skip to Main content Skip to Navigation
New interface
Conference papers

Weighted partitions

Abstract : 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 S_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.
Document type :
Conference papers
Complete list of metadata

https://hal.inria.fr/hal-01229690
Contributor : Alain Monteil Connect in order to contact the contributor
Submitted on : Tuesday, November 17, 2015 - 10:20:00 AM
Last modification on : Tuesday, March 7, 2017 - 3:23:22 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:39:21 AM

File

dmAS0187.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Rafael González S. d'León, Michelle L. Wachs. Weighted partitions. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1029-1040, ⟨10.46298/dmtcs.2363⟩. ⟨hal-01229690⟩

Share

Metrics

Record views

38

Files downloads

955