Tropical integrable systems and Young tableaux: Shape equivalence and Littlewood-Richardson correspondence

TL;DR

This paper introduces a novel characterization of Young tableaux's shape equivalence and Littlewood-Richardson correspondence using tropical integrable systems, providing an alternative proof of the shape change theorem.

Contribution

It offers a new tropical integrable systems approach to understanding Young tableaux and their combinatorial properties, including an alternative proof of a key theorem.

Findings

New characterization of shape equivalence classes

Tropical approach to Littlewood-Richardson correspondence

Alternative proof of the shape change theorem

Abstract

We present a new characterization of the shape equivalent class and the Littlewood-Richardson correspondence of Young tableaux in terms of tropical (ultradiscrete) integrable systems. As an application, an alternative proof of the "shape change theorem" is given.