4 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 $T=(a_1^{\varepsilon_1},\dots,a_n^{\varepsilon_n})$ be a virtual rational tangle, where the $a_i$ are the tangle parameters and each $\varepsilon_i$ records the corresponding v…

Let $T$ be a virtual rational tangle, and let $C(T)$ denote its conductance. Two virtual rational tangles are $F$-equivalent when they are related by the equivalence generated by t…

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 $\tau$…