Bracket polynomials of torus links as Fibonacci polynomials. (English) Zbl 1470.57003

Summary: In this paper we work the bracket polynomial of \((2, n)\)-torus link as a Fibonacci polynomial. We show that the bracket polynomial of \((2, n)\)-torus link provides recurrence relation as similar to the Fibonacci polynomial and give its some fundamental properties. We also prove important identities, which are similar to the Fibonacci identities, for the bracket polynomial of \((2, n)\)-torus link and prove Fibonacci-like identities of the Jones polynomial of \((2, n)\)-torus link as a result of the bracket polynomial. Finally, we observe that the bracket polynomial of \((2, n)\)-torus link and therefore its Jones polynomial can be derived from its Alexander-Conway polynomial or classical Fibonacci polynomial.


57K10 Knot theory
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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