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Noncommutative symmetric functions with matrix parameters (1110.3209v1)
Published 14 Oct 2011 in math.CO
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.