Identities of the Kauffman Monoid $\mathcal{K}_3$

TL;DR

This paper provides a clear combinatorial description of the identities of the Kauffman monoid 3, enabling an efficient polynomial-time algorithm to verify if an identity holds.

Contribution

It offers the first transparent combinatorial characterization of 3's identities, facilitating efficient identity verification.

Findings

Combinatorial characterization of 3's identities

Polynomial-time algorithm for identity checking

Enhanced understanding of Kauffman monoid structure

Abstract

We give a transparent combinatorial characterization of the identities satisfied by the Kauffman monoid $\mathcal{K}_3$. Our characterization leads to a polynomial time algorithm to check whether a given identity holds in $\mathcal{K}_3$.