Schützenberger's factorization on the (completed) Hopf algebra of $q-$stuffle product.

Chen Bui (1) , Gérard Henry Edmond Duchamp (2) , Vincel Hoang Ngoc Minh (2)

1 Hué University, College of sciences
2 LIPN - Laboratoire d'Informatique de Paris-Nord

In order to extend the Schützenberger's factorization, the combinatorial Hopf algebra of the $q$-stuffles product is developed systematically in a parallel way with that of the shuffle product and and in emphasizing the Lie elements as studied by Ree. In particular, we will give here an effective construction of pair of bases in duality.

Mots clés: Shuffle; Lyndon words; Lie elements; transcendence bases.; transcendence bases

Domaines: Combinatoire [math.CO]; Calcul formel [cs.SC]

Chen Bui, Gérard Henry Edmond Duchamp, Vincel Hoang Ngoc Minh. Schützenberger's factorization on the (completed) Hopf algebra of $q-$stuffle product.. 2013. ⟨hal-00823968⟩