2 problems

Let $D$ be a reduced alternating diagram of a knot $K$ with determinant $p$, where $p$ is prime. A Fox $p$-coloring is a coloring of the arcs of $D$ by elements of $\mathbb Z_p$ sa…

Prime-modulus minimum-color conjecture. If $\langle r,\det L\rangle=\langle r,\det L'\rangle$, then $mincol_rL=mincol_rL'$. Moreover, $m_p$ is a non-decreasing function of the prim…