HOMFLY polynomials of torus links as generalized Fibonacci polynomials
type: Item
instance of: scholarly article
title: HOMFLY polynomials of torus links as generalized Fibonacci polynomials
zbMATH Open document ID: 1326.57022
author: Kemal Taşköprü
author: Ismet Altintas
published in: The Electronic Journal of Combinatorics
publication date: 2015-11-02T00:00:00Z
full work available at URL: v22i4p8
review text: Summary: 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.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 6502794
zbMATH Keywords: HOMFLY polynomial
zbMATH Keywords: Alexander-Conway polynomial
zbMATH Keywords: torus link
zbMATH Keywords: Fibonacci polynomial
zbMATH Keywords: Binet's formula
zbMATH Keywords: Fibonacci identities
MaRDI profile type: Publication
cites work: An oriented state model for the Jones polynomial and its applications alternating links
cites work: Generalized Fibonacci polynomials and fibonomial coefficients
cites work: Q3105385
cites work: A polynomial invariant for unoriented knots and links
cites work: Q5601331
cites work: Q5331777
cites work: Fibonacci identities via the determinant of tridiagonal matrix
cites work: Free differential calculus. I: Derivation in the free group ring
cites work: A new polynomial invariant of knots and links
cites work: Q5650405
cites work: Q4320535
cites work: A polynomial invariant for knots via von Neumann algebras
cites work: On Knots. (AM-115)
cites work: State models and the Jones polynomial
cites work: New Invariants in the Theory of Knots
cites work: An Invariant of Regular Isotopy
cites work: On Fibonacci Knots
cites work: Q4886696
cites work: On generalized Fibonacci and Lucas polynomials
description: scientific article; zbMATH DE number 6502794