The immaculate basis of the non-commutative symmetric functions (Extended Abstract)

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. © 2013 Discrete Mathematics and Theoretical Computer Science (DMTCS).