Noncommutative symmetric functions with matrix parameters

Abstract

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.

Keywords

• macdonald polynomials
• noncommutative symmetric functions
• quasi-symmetric functions
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]