Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

Gérard Henry Edmond Duchamp (1) , Florent Hivert (2) , Jean-Christophe Novelli (3) , Jean-Yves Thibon (3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.

Domaines: Combinatoire [math.CO]

Gérard Henry Edmond Duchamp, Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited. 2008. ⟨hal-00325270⟩