HOMFLY polynomials of torus links as generalized Fibonacci polynomials

Creative Commons License

TAŞKÖPRÜ K., Altıntaş İ.

Electronic Journal of Combinatorics, vol.22, no.4, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.37236/5324
  • Journal Name: Electronic Journal of Combinatorics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Alexander-Conway polynomial, Binet’s formula, Fi-bonacci polynomial, Fibonacci identities, HOMFLY polynomial, Torus link
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2015, Australian National University. All rights reserved.The focus of this paper is to study the HOMFLY polynomial of (2, n)-torus link as a generalized Fibonacci polynomial. For this purpose, we first introduce a form of generalized Fibonacci and Lucas polynomials and provide their some fundamental properties. We define the HOMFLY polynomial of (2, n)-torus link with a way similar to our generalized Fibonacci polynomials and provide its fundamental properties. We also show that the HOMFLY polynomial of (2, n)-torus link can be obtained from its Alexander-Conway polynomial or the classical Fibonacci polynomial. We finally give the matrix representations and prove important identities, which are similar to the Fibonacci identities, for the our generalized Fibonacci polynomial and the HOMFLY polynomial of (2,n)-torus link.