Ordering the Reidemeister moves of a classical knot

TL;DR

This paper proves that any two diagrams of the same knot or link can be transformed into each other through a sequence of Reidemeister moves arranged in a specific order by move type.

Contribution

It introduces a method to order Reidemeister moves of a knot diagram, providing a structured approach to knot diagram transformations.

Findings

Reidemeister moves can be sequenced by type to connect equivalent diagrams.

The ordering simplifies understanding of knot transformations.

The result applies to all classical knots and links.

Abstract

We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type.