A bound for orderings of Reidemeister moves (Q371262)

Finitely many Reidemeister moves of type I, II and III connect any two diagrams representing the same link, indeed a fundamental result in classical knot theory. A. Coward showed that these can be chosen to form a sequence of moves of types I, II, III, II, I in this order, where the first two increase, while the last two decrease the number of crossings [\textit{A. Coward}, Algebr. Geom. Topol. 6, 659--671 (2006; Zbl 1095.57005)]. Based on this work, the author gives an upper estimate of the number of moves necessary. The argument is directly geometric using so-called tails and lollipops to unite Reidemeister moves and keep track of their number.