Generalized binomial coefficients related to special number sequences

In this thesis, Fibonacci, Lucas, Pell, Pell-Lucas and tribonacci number sequences, which are special number sequences, and their associated polynomials and associated binomial coefficients are studied. In addition, gibonomial coefficients, which are binomial coefficients created with Fibonacci polynomials, are given. This thesis consists of seven chapters. In the first chapter, literature information about the study is given. In the second chapter, basic information about the study, definitions and theorems are given. In the third chapter, binomial coefficients and their properties are examined. In the fourth chapter, Fibonomial coefficients and Gaussian binomial coefficients, which are generalized binomial coefficients, are given in detail. In the fifth chapter, Fibonacci polynomials, Lucas polynomials, Pell polynomials, Pell-Lucas polynomials, tribonacci polynomials and gibonacci (generalized Fibonacci) polynomials, which are polynomials associated with special number sequences, are studied. Finally, in the sixth section, gibonomial coefficients, which are binomial coefficients associated with Fibonacci polynomials, are given. In the seventh chapter, the Conclusion and Suggestions, the study is summarized, evaluations are made and some suggestions are made regarding the future studies.