An algorithmic Littlewood-Richardson rule

TL;DR

This paper introduces an algorithmic Littlewood-Richardson rule that provides a new combinatorial interpretation and proof of a geometric rule, connecting skew Young diagrams with Specht modules.

Contribution

It presents a novel algorithmic deformation approach to the Littlewood-Richardson rule, establishing a bijection with the classical rule and offering new insights into Specht modules.

Findings

Provides a new combinatorial interpretation of the geometric Littlewood-Richardson rule

Establishes a bijection with the classical rule using skew Young diagrams

Includes a corollary related to Specht modules of intermediate diagrams

Abstract

We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorial interpretation and proof of the geometric rule presented by Coskun. We also present a corollary regarding the Specht modules of the intermediate diagrams.