Reidemister的最小序列移动使$(n+1,n)$ -环面纽结的图变为$(n,n+1)$ -环面纽结的图
The minimal sequence of Reidemister moves bringing the diagram of $(n+1,n)$-torus knot to that of $(n,n+1)$-torus knot
摘要：
令$D(p,q)$为$(p,q)$ -环面结的通常结图，即$D(p,q)$为$p$ -编织$(σ_1^{-1} σ_2^{-1}... σ_{p-1}^{-1})^q$的闭包。众所周知，$D(p,q)$和$D(q,p)$代表同一个结。结果表明，$D(n+1,n)$可以通过一系列的$\{(n-1)n(2n-1)/6 \} + 1$ Reidemeister移动，其中包括一个单一的RI移动和$(n-1)n(2n-1)/6$ RIII移动变形为$D(n,n+1)$。使用贝壳，我们表明，这个序列是最小的所有序列，使$D(n+1,n)$的$D(n,n+1)$。
英文摘要：
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 $(σ_1^{-1} σ_2^{-1}... σ_{p-1}^{-1})^q$. As is well-known, $D(p,q)$ and $D(q,p)$ represent the same knot. It is shown that $D(n+1,n)$ can be deformed to $D(n,n+1)$ by a sequence of $\{(n-1)n(2n-1)/6 \} + 1$ Reidemeister moves, which consists of a single RI move and $(n-1)n(2n-1)/6$ RIII moves. Using cowrithe, we show that this sequence is minimal over all sequences which bring $D(n+1,n)$ to $D(n,n+1)$.
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