The OU number and Reidemeister moves of type III for link diagrams

TL;DR

This paper introduces the OU number and non-self OU sequence for link diagrams, providing a new lower bound on the number of Reidemeister type III moves needed to transform one diagram into another.

Contribution

It presents novel invariants, the OU number and non-self OU sequence, to estimate Reidemeister move complexity between link diagrams.

Findings

The OU number offers a quantifiable lower bound for Reidemeister III moves.

The non-self OU sequence enhances understanding of link diagram transformations.

Provides a method to compare link diagrams based on these invariants.

Abstract

We introduce the non-self OU sequence and the OU number for link diagrams. Using these, we give a lower bound for the number of necessary Reidemeister moves of type III between two diagrams of the same link.