Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials
arXiv:1107.5516
Abstract
The explicit formula, which expresses the Alexander polynomials Δ_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials Δ_{k,2}(t) of torus knots T(k,2), is found. Using this result and those from our previous papers, we express the Alexander polynomials Δ_{n,3}(t) through Chebyshev polynomials. The latter result is extended to general torus knots T(n,l) with n and l coprime.
8 pages, two-column ujp style; http://www.ujp.bitp.kiev.ua