Geodesic
Transitive Hall Sets
Séminaire lotharingien de combinatoire, Tome 54 (2006-2007)

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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. 

@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},
     publisher = {mathdoc},
     volume = {54},
     year = {2006-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a10/}
}
TY  - JOUR
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AU  - Marianne Flouret
AU  - Jean-Gabriel Luque
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JO  - Séminaire lotharingien de combinatoire
PY  - 2006-2007
VL  - 54
PB  - mathdoc
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ID  - SLC_2006-2007_54_a10
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%A Jean-Gabriel Luque
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%F SLC_2006-2007_54_a10
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/