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.
@article{10_37236_5324,
author = {Kemal Ta\c{s}k\"opr\"u and \.Ismet Alt{\i}nta\c{s}},
title = {HOMFLY polynomials of torus links as generalized {Fibonacci} polynomials},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5324},
zbl = {1326.57022},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5324/}
}
TY - JOUR
AU - Kemal Taşköprü
AU - İsmet Altıntaş
TI - HOMFLY polynomials of torus links as generalized Fibonacci polynomials
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5324/
DO - 10.37236/5324
ID - 10_37236_5324
ER -
%0 Journal Article
%A Kemal Taşköprü
%A İsmet Altıntaş
%T HOMFLY polynomials of torus links as generalized Fibonacci polynomials
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5324/
%R 10.37236/5324
%F 10_37236_5324
Kemal Taşköprü; İsmet Altıntaş. HOMFLY polynomials of torus links as generalized Fibonacci polynomials. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5324
