2 problems

Let $L$ be a two-component link, let $b$ be a band, and let $K_b$ be the oriented knot obtained from $L$ by band surgery along $b$. For each $n\in\mathbf{Z}$, let $K_{b+n}$ be the…

A banding of the unknot is a band surgery on the unknot that produces an alternating link. An almost alternating diagram of the unknot is an alternating diagram with one dealternat…