10.46298/dmtcs.2363
D'León, Rafael González S.
Rafael González S.
D'León
Wachs, Michelle L.
Michelle L.
Wachs
Weighted partitions
episciences.org
2013
poset topology
partitions
free Lie algebra
rooted trees
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
contact@episciences.org
episciences.org
2016-11-21T15:44:48+01:00
2021-09-30T22:03:38+02:00
2013-01-01
en
Journal article
https://dmtcs.episciences.org/2363
https://hal.archives-ouvertes.fr/hal-01229690v1
1365-8050
PDF
1
Discrete Mathematics & Theoretical Computer Science ; DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) ; Proceedings ; 1365-8050
International audience
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.