Unoriented knot polynomials of torus links as Fibonacci-Type polynomials

Altlntaş I., TAŞKÖPRÜ K.

Asian-European Journal of Mathematics, vol.12, no.4, 2019 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1142/s1793557119500530
  • Journal Name: Asian-European Journal of Mathematics
  • Journal Indexes: Scopus
  • Keywords: BLM/Ho polynomial, explicit form, generating function, Kauffman polynomials, recurrence relation, Vieta polynomials
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2019 World Scientific Publishing Company.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.