On bracket polynomials as Fibonacci polynomials

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. Bracket polynomial and normalized bracket polynomial of them have been discussed in detail in the third chapter. Studies to establish a relationship between knot polynomials and Fibonacci polynomial have been done in the fourth chapter. A generalized Fibonacci polynomial which its initial conditions are the same as Fibonacci polynomial has been introduced in this chapter. In the fifth chapter, it has been first proved that the sequence of bracket polynomial of (2,n)–torus link satisfies a recurrence relation. Then, the Fibonacci-like properties of the bracket polynomial of (2,n)–torus link has been proved. By using the generalized Fibonacci sequence introduced in chapter four, some sums properties of the bracket polynomial of (2,n)–torus link has been found and proven. In addition, from the Fibonacci properties of the bracket polynomial of (2,n)–torus link, its Fibonacci-like properties of the normalized polynomial and hence of Jones polynomials have been obtained.