Pieri rules for skew dual immaculate functions

TL;DR

This paper establishes Pieri rules for skew dual immaculate functions and their row-strict variants, expanding the combinatorial framework for these functions using Hopf algebra techniques.

Contribution

It introduces Pieri rules for skew dual immaculate functions and their row-strict counterparts, utilizing a right-action approach related to skew Littlewood-Richardson rules.

Findings

Pieri rules for skew dual immaculate functions derived

Pieri rules for row-strict (dual) immaculate functions established

Uses Hopf algebra techniques to prove the rules

Abstract

In this paper we give Pieri rules for skew dual immaculate functions and their recently discovered row-strict counterparts. We establish our rules using a right-action analogue of the skew Littlewood-Richardson rule for Hopf algebras of Lam-Lauve-Sottile. We also obtain Pieri rules for row-strict (dual) immaculate functions.