Unoriented knot polynomials of torus links as Fibonacci-type polynomials

Abstract

The focus of this paper is to study the two-variable Kauffman polynomials L and F, and the one-variable BLM/Ho polynomial Q of (2, n)-torus link as the Fibonacci-type polynomials and to express the Kauffman polynomials in terms of the BLM/Ho polynomial. For this purpose, we prove that each of the examined polynomials of (2, n)-torus link can be determined by a third-order recurrence relation and give the recursive properties of them. We correlate these polynomials with the Fibonacci-type polynomials. By using the relations between the BLM/Ho polynomials and Fibonacci-type polynomials, we express the Kauffman polynomials in terms of the BLM/Ho polynomials.