11 problems

Let $p$ be a prime, and let a knot have a reduced alternating diagram with determinant $p$. A non-trivial $p$-coloring is a labeling of the diagram's arcs by elements of…

Let two links in $S^3$ be equivalent in the cubic skein module, meaning that they represent the same element of the cubic skein module. Cubic skein determination of Fox 7-colorings…

The $C[24]$ equivalence-class conjecture. The set

$C[6,1]$–$C[6,2]$ equivalence conjecture.

Universal quandle-coloring separation conjecture. There exists such a sequence satisfying, for all knots $K,K'$,

Finite-quandle separation conjecture. There exists such a sequence $\mathcal S$ satisfying, for all $K,K'\in\mathcal K$,

Dual Alexander quandle coloring conjecture. For every connected Alexander quandle $Q$,

KH–pseudoalternating conjecture. A pseudodiagram with the KH property cannot be pseudoalternating.

Virtual-knot separation conjecture. For any pair of non-isomorphic Galkin quandles, there is a virtual knot with different numbers of colorings by the two quandles.

Equal-coloring-count conjecture. The listed Galkin quandles have the same numbers of colorings for all knots.

$C[6,2]$ coloring conjecture. If a knot is 3-colorable, then it is non-trivially colored by $C[6,2]$.