The immaculate basis of the non-commutative symmetric functions

Published 20 Mar 2013 in math.CO | (1303.4801v1)

Abstract: FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula.

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