Quasisymmetric and noncommutative skew Pieri rules

TL;DR

This paper derives new skew Pieri rules for skew quasisymmetric and noncommutative Schur functions using Hopf algebraic techniques, generalizing and recovering previous results.

Contribution

It introduces a unified Hopf algebraic approach to derive skew Pieri rules for both skew quasisymmetric and noncommutative Schur functions, extending prior work.

Findings

Derived skew Pieri rules for skew quasisymmetric Schur functions.

Established skew Pieri rules for skew noncommutative Schur functions.

Unified the derivation process using Hopf algebraic techniques.

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.