Combinatorial knot invariants that detect trefoils
We construct a series of combinatorial quandle-like knot invariants. We color regions of a knot diagram rather than lines and assign a weight to each coloring. Sets of these weights are the invariants we construct (colorings and weights depend on several parameters).
Using these invariants, we prove that left and right trefoils are not isotopic using this invariant (in a particular case).