Patterns of the V2-Polynomial of Knots

Recently, Kashaev and the first author constructed an R-matrix from a Nichols algebra with an automorphism, that leads, via the Reshetikhin–Turaev functor, to a multivariable polynomial invariant of knots. Applying this to a rank 2 Nichols algebra, results in a sequence Vn of 2-variable knot polynomials with integer coefficients, the first polynomial been identified with the Links–Gould polynomial. In this note we present the results of the computation of the Vn-polynomials for n=1,2,3,4. This leads to the discovery of emerging patterns, including the genus bound for V2 being an equality for all 352.2 million knots with at most 19 crossings, as well as unexpected Conway mutations that seem undetected by the Vn-polynomials as well as by Heegaard Floer Homology and Khovanov Homology.