45 citations · 155 across the 17 of their papers we have counts for
4 papers · 2 filters
Combinatorial expansions for families of non-commutative k-Schur functions
Chris Berg, Franco Saliola, Luis Serrano
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 combina…
A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions
Chris Berg, Nantel Bergeron, Franco Saliola +2
We introduce a new basis of the non-commutative symmetric functions whose commutative images are Schur functions. Dually, we build a basis of the quasi-symmetric functions which ex…
Quasi-symmetric and non-commutative affine Schur functions
Chris Berg, Luis Serrano
We introduce dual Hopf algebras which simultaneously combine the concepts of the k-Schur function theory with the quasi-symmetric Schur function theory. We construct dual basis of…
Pieri operators on the affine nilCoxeter algebra
Chris Berg, Franco Saliola, Luis Serrano
We study a family of operators on the affine nilCoxeter algebra. We use these operators to prove conjectures of Lam, Lapointe, Morse, and Shimozono regarding strong Schur functions…