HOMFLY polynomials of torus links as generalized Fibonacci polynomials

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TAŞKÖPRÜ K., Altıntaş İ.

Electronic Journal of Combinatorics, cilt.22, sa.4, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 4
  • Basım Tarihi: 2015
  • Doi Numarası: 10.37236/5324
  • Dergi Adı: Electronic Journal of Combinatorics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Alexander-Conway polynomial, Binet’s formula, Fi-bonacci polynomial, Fibonacci identities, HOMFLY polynomial, Torus link
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

© 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.