Is there a list of numbers of how many knots are disinguished by their Alexander polynomials? Up to certain crossing numbers, or for each crossing number individually. I`m trying to get a feel for how likely it is to be able to tell apart a knot just based on one polynomial. Of course it is possible to count by hand, but for the higher crossing numbers...
I also wondering whether it is possible to get this numbers using the Knottheory package for Mathematica using NumberOfKnots[n].
The table gives the number of occuring Alexander polynomials if the knots are regarded for each crossing number seperately. This is according to mathematica and Knottheory package, it might be good to check with other tables.