Abstract
In this extended abstract we consider the poset of weighted partitions ∏wn , introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of ∏wn 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 ∏wnhas a nice factorization analogous to that of ∏n.
Original language | English (US) |
---|---|
Pages (from-to) | 1029-1040 |
Number of pages | 12 |
Journal | Discrete Mathematics and Theoretical Computer Science |
State | Published - Nov 18 2013 |
Event | 25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France Duration: Jun 24 2013 → Jun 28 2013 |
Keywords
- Free lie algebra
- Partitions
- Poset topology
- Rooted trees
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
- Discrete Mathematics and Combinatorics