Quasisymmetric and noncommutative skew Pieri rules

Abstract

In this note we derive skew Pieri rules in the spirit of Assaf–McNamara for skew quasisymmetric Schur functions using the Hopf algebraic techniques of Lam–Lauve–Sottile, and recover the original rules of Assaf–McNamara as a special case. We then apply these techniques a second time to obtain skew Pieri rules for skew noncommutative Schur functions.