Transitive Hall sets

Gérard Henry Edmond Duchamp (1) , Marianne Deboysson-Flouret (2) , Jean-Gabriel Luque (3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LIH - Laboratoire d'informatique du Havre
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Mots clés: Partially Commutative Structures; Hall sets; Free Lie Algebra; Partially Commutative Structures.

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]; Informatique et langage [cs.CL]; Théorie et langage formel [cs.FL]

Gérard Henry Edmond Duchamp, Marianne Deboysson-Flouret, Jean-Gabriel Luque. Transitive Hall sets. Seminaire Lotharingien de Combinatoire, 2006, 54, 19pp. ⟨hal-00005781⟩