### Abstract

We explore the well-known relationship between the representations of the symmetric group on the homology of the partition lattice and on the 1^{n} 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.

Original language | English (US) |
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Pages (from-to) | 287-319 |

Number of pages | 33 |

Journal | Discrete Mathematics |

Volume | 193 |

Issue number | 1-3 |

DOIs | |

State | Published - Nov 28 1998 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics