Adnan

The leading coefficient of the Alexander polynomial of twisted torus knots

For a twisted torus knot K(p,q;r,s) with gcd(p,q) = 1 and 2 ≤ r < p we determine the leading coefficient of the Alexander polynomial Δ exactly. Writing Δ up to a unit as Δ̃(u) = Σ_{m=0}^{r−1} γ_m(t) u^m with u = t^{rs}, we prove a multiset law expressing each γ_m as a sum of p monomials with all coefficients +1, a clos...