A bound for orderings of Reidemeister moves
Julian Gold · Algebraic & Geometric Topology · 2013
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. 57M25In 1927 Kurt Reidemeister proved that any two link diagrams representing the same link may be joined by a finite sequence of Reidemeister moves.The importance of this theorem to knot theory cannot be overstated.Mathematicians like Alexander Coward [1; 2], Marc Lackenby [2], Bruce Trace [4], and Joel Hass and Jeffery Lagarias [3] have all explored properties of sequences of Reidemeister moves.