k-Fibonacci numbers and on Jones polynomials of (2,n)-torus links

It has been given a short literature information about the knot polynomials and the Fibonacci sequences in the first chapter. Some fundamental concepts and properties have been given in the second chapter. k-Fibonacci sequence whether to give, properties of them have been discussed in detail in the third chapter. The Fibonacci polynomial in the fourth chapter and the polynomials obtained from derivatives of the Fibonacci polynomial and the number sequences produced from these polynomial has been examined in the fifth chapter. Studies to establish a relationship between knot polynomials and Fibonacci polynomial have been done in the sixth chapter. A generalized Fibonacci polynomial, which its initial conditions are the same as Fibonacci polynomial has been introduced in this chapter. By using this polynomial, the Jones polynomial of (2,n)-torus link has been expressed as a generalized Fibonacci polynomial. Firstly, it has been proved that the sequence of the Jones polynomials of (2,n)-torus link satisfy a recurrence relation. Then, it has been given Fibonacci-like properties, matrix representations and links. Consequently, the Jones polynomial of (2,n)-torus link has been obtained as a generalized Fibonacci polynomial.