Article - post-print
We give a new interpretation of the Alexander polynomial Δ0 for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ0 determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.
Mellor, B., 2016: Alexander and writhe polynomials for virtual knots. J. Knot Theory Ramif., 25.8, arXiv:1601.07153.