Alexander Polynomial Invariants of Torus Knots T(n, 3) and Chebyshev Polynomials

Authors

  • A.M. Gavrilik Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • A.M. Pavlyuk Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe56.7.680

Keywords:

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Abstract

The explicit formula, which expresses the Alexander polynomials n,3(t) of torus knots T(n, 3) as a sum of the Alexander polynomials 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 n,3(t) through Chebyshev polynomials. The latter result is extended to general torus knots T(n, l) with n and l coprime.

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Published

2022-02-09

How to Cite

Gavrilik, A., & Pavlyuk, A. (2022). Alexander Polynomial Invariants of Torus Knots T(n, 3) and Chebyshev Polynomials. Ukrainian Journal of Physics, 56(7), 680. https://doi.org/10.15407/ujpe56.7.680

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Section

General problems of theoretical physics