Products of Factorial Schur Functions

TL;DR

This paper introduces a new rule for expanding products of factorial Schur functions into Schur functions, generalizing classical and recent combinatorial rules, with implications for algebraic combinatorics.

Contribution

It provides a generalized rule for computing coefficients in factorial Schur function products, extending the Molev-Sagan and Littlewood-Richardson rules.

Findings

Derived a new combinatorial rule for factorial Schur functions

Unified previous rules into a broader framework

Facilitated calculations in algebraic combinatorics

Abstract

The product of any finite number of factorial Schur functions can be expanded as a $Z[y]$-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion which generalizes a specialization of the Molev-Sagan rule, which in turn generalizes the classical Littlewood-Richardson rule.