A Littlewood-Richardson Type Rule for Row-Strict Quasisymmetric Schur Functions

TL;DR

This paper develops a Littlewood-Richardson type rule for expanding products involving row-strict quasisymmetric Schur functions, based on new properties of an insertion algorithm for composition tableaux.

Contribution

It introduces a novel rule for multiplying row-strict quasisymmetric Schur functions with symmetric Schur functions, expanding understanding of their algebraic structure.

Findings

Derived a Littlewood-Richardson type rule for these functions

Identified new properties of Mason and Remmel's insertion algorithm

Enhanced the combinatorial understanding of row-strict quasisymmetric Schur functions

Abstract

We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new properties of an insertion algorithm defined by Mason and Remmel (2010) which inserts a positive integer into a row-strict composition tableau.