We explore the well-known relationship between the representations of the symmetric group on the homology of the partition lattice and on the 1n component of the free Lie algebra. We give two new combinatorial proofs of the sign twisted isomorphism between the two modules. One involves a bijection between bases and the other involves a bijection between generating sets which takes relations to relations.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics