Unoriented knot polynomials of torus links as Fibonacci-Type polynomials

Altlntaş I., TAŞKÖPRÜ K.

Asian-European Journal of Mathematics, cilt.12, sa.4, 2019 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s1793557119500530
  • Dergi Adı: Asian-European Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Anahtar Kelimeler: BLM/Ho polynomial, explicit form, generating function, Kauffman polynomials, recurrence relation, Vieta polynomials
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

© 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.