Another proof of the alternating sign matrix conjecture

TL;DR

This paper provides a new proof of Robbins' conjecture on the enumeration of alternating sign matrices using the six-vertex model and Yang-Baxter equation, offering an alternative mathematical approach.

Contribution

It introduces a novel proof method for the alternating sign matrix conjecture based on statistical mechanics models and integrable systems.

Findings

Confirmed the enumeration formula for alternating sign matrices.

Demonstrated the application of the Yang-Baxter equation in combinatorial proofs.

Provided insights into the connection between ice models and matrix enumeration.

Abstract

Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result using an analysis of the six-vertex state model (also called square ice) based on the Yang-Baxter equation.