2 problems

Let $[n_1,n_2,\dots,n_r]$ and $\epsilon[n_1,n_2,\dots,n_r]$ be two diagrams of rational links, where $\epsilon=1$ if $r$ is odd and $\epsilon=-1$ otherwise. The Rational Tangle Alg…

Let $\tau$ be a tangle, and let $\alpha_0$ and $\alpha_1$ be sites for a rational subtangle replacement (RSR) on $\tau$. Suppose their lifts to the branched double cover of $\tau$…