The minimal sequence of Reidemister moves bringing the diagram of $(n+1,n)$-torus knot to that of $(n,n+1)$-torus knot

Chuichiro Hayashi, Miwa Hayashi

Let $D(p,q)$ be the usual knot diagram of the $(p,q)$-torus knot, that is, $D(p,q)$ is the closure of the $p$-braid $({\sigma }_1^{-1}{\sigma }_2^{-1}...{\sigma }_{p-1}^{-1}{)}^q$. As is well-known, $D(p,…