#####
Séminaire Lotharingien de Combinatoire, B54k (2006), 19 pp.

# Gérard Duchamp, Marianne Flouret and Jean-Gabriel Luque

# Transitive Hall Sets

**Abstract.**
We give the definition of Lazard and Hall sets in the context of
transitive factorizations of free monoids. The equivalence of the
two properties is proved. This allows to build new effective bases
of free partially commutative Lie algebras. The commutation graphs
for which such sets exist are completely characterized and we
explicit, in this context, the classical PBW rewriting process.

Received: June 30, 2005.
Revised: May 26, 2006.
Accepted: July 7, 2006.

The following versions are available: