Multiplicative structures of the immaculate basis of non-commutative symmetric functions

We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the Schur basis for the algebra of symmetric functions, and it shares many of its wonderful properties. For instance, in this article we describe non-commutati

Combinatorial expansions for families of non-commutative k-Schur functions

We apply down operators in the affine nilCoxeter algebra to yield explicit combinatorial expansions for certain families of non-commutative k-Schur functions. This yields a combinatorial interpretation for a new family of k-Littlewood-Richardson coefficients.