Which notation unambigously describes a knot?

Question

For a chiral knot the Dowker notations for the knot and it's mirror image are the same. So the Dowker notation does not convey the information of chirality. I am wondering is there any notation that does?

Answer 1

To solve this, we introduce the concept of handedness of a crossing, as in left handed or right handed crossings. To define this, we orient our knot, and rotate the knot so both arcs are "point up." If the arc that starts on the right and goes left is over, it is a right handed crossing. The other is a left handed crossing. See the pictures here.

Now that we know what handedness is, a knot and its mirror image have exactly the opposite handedness at every crossing. So we can add this notation to each entry of the Dowker notation, with say a superscript. This will eliminate the ambiguity. Also, the Extended Gauss Code does this too.