Abstract
In this extended abstract we consider the poset of weighted partitions ∏w n , introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of ∏w n 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 ∏w nhas 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 - 2013 |
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Keywords
- Free lie algebra
- Partitions
- Poset topology
- Rooted trees
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
- Computer Science(all)
Cite this
On the poset of weighted partitions. / D'León, Rafael S González; Galloway, Michelle L.
In: Discrete Mathematics and Theoretical Computer Science, 2013, p. 1029-1040.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the poset of weighted partitions
AU - D'León, Rafael S González
AU - Galloway, Michelle L
PY - 2013
Y1 - 2013
N2 - In this extended abstract we consider the poset of weighted partitions ∏w n , introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of ∏w n 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 ∏w nhas a nice factorization analogous to that of ∏n.
AB - In this extended abstract we consider the poset of weighted partitions ∏w n , introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of ∏w n 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 ∏w nhas a nice factorization analogous to that of ∏n.
KW - Free lie algebra
KW - Partitions
KW - Poset topology
KW - Rooted trees
UR - http://www.scopus.com/inward/record.url?scp=84887500249&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84887500249&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84887500249
SP - 1029
EP - 1040
JO - Discrete Mathematics and Theoretical Computer Science
JF - Discrete Mathematics and Theoretical Computer Science
SN - 1365-8050
ER -