Authors: Alain Lascoux ¹; Jean-Christophe Novelli ¹; Jean-Yves Thibon ¹

• 1 Laboratoire d'Informatique Gaspard-Monge

We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices then give back the two-vector families of Hivert, Lascoux, and Thibon and the noncommutative Macdonald functions of Bergeron and Zabrocki.