episciences.org_2363_1639044301
1639044301
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
01
01
2013
DMTCS Proceedings vol. AS,...
Proceedings
Weighted partitions
Rafael González S.
D'León
Michelle L.
Wachs
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.
01
01
2013
2363
https://hal.archives-ouvertes.fr/hal-01229690v1
10.46298/dmtcs.2363
https://dmtcs.episciences.org/2363