2 problems

Let $K$ be a knot, let $\overline{K}$ denote its mirror image, and let $-\overline{K}$ denote the mirror image with reversed orientation. The Kauffman polynomial of $K$ is denoted…

For each integer $k\geq 1$, let $E_{2k+1}$ denote the family of alternating knots that embed on an $M_{2k+1}$ mosaic with $|D|=2$, where $D$ is the relevant dual structure. A knot…