A bound for orderings of Reidemeister moves

TL;DR

This paper establishes an upper limit on the number of ordered Reidemeister moves needed to transform one link diagram into another, based on the total number of unordered moves required, aiding understanding of link diagram transformations.

Contribution

It introduces a bound relating ordered and unordered Reidemeister moves, providing a new quantitative measure for link diagram transformations.

Findings

Derived an explicit upper bound for ordered Reidemeister moves

Connected ordered move count to unordered move count

Enhanced understanding of link diagram transformation complexity

Abstract

We provide an upper bound on the number of ordered Reidemeister moves required to pass between two diagrams of the same link. This bound is in terms of the number of unordered Reidemeister moves required.