Immaculate basis of the non-commutative symmetric functions

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.

Keywords

• non-commutative symmetric functions
• quasi-symmetric functions
• tableaux
• schur functions
• [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]