A bijectional attack on the Razumov-Stroganov conjecture

TL;DR

This paper explores a bijectional approach to prove the Razumov-Stroganov conjecture, presenting techniques that, while currently unsuccessful, could potentially lead to a proof.

Contribution

Introduces a novel bijectional method aimed at proving the Razumov-Stroganov conjecture, offering new techniques for future research.

Findings

Proposed a bijectional approach to the conjecture

Developed new techniques with potential for proof

Unsuccessful in proving the conjecture but laid groundwork

Abstract

We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.