The immaculate basis of the non-commutative symmetric functions

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.

arXiv admin note: substantial text overlap with arXiv:1208.5191