Geodesic
Transitive Hall Sets
Séminaire lotharingien de combinatoire, Tome 54 (2006-2007) 
Gérard Duchamp; Marianne Flouret; Jean-Gabriel Luque. Transitive Hall Sets. Séminaire lotharingien de combinatoire, Tome 54 (2006-2007). http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a10/
@article{SLC_2006-2007_54_a10,
     author = {G\'erard Duchamp and Marianne Flouret and Jean-Gabriel Luque},
     title = {Transitive {Hall} {Sets}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2006-2007},
     volume = {54},
     url = {http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a10/}
}
TY  - JOUR
AU  - Gérard Duchamp
AU  - Marianne Flouret
AU  - Jean-Gabriel Luque
TI  - Transitive Hall Sets
JO  - Séminaire lotharingien de combinatoire
PY  - 2006-2007
VL  - 54
UR  - http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a10/
ID  - SLC_2006-2007_54_a10
ER  - 
%0 Journal Article
%A Gérard Duchamp
%A Marianne Flouret
%A Jean-Gabriel Luque
%T Transitive Hall Sets
%J Séminaire lotharingien de combinatoire
%D 2006-2007
%V 54
%U http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a10/
%F SLC_2006-2007_54_a10

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.