arXiv subjects
Publications and source records attributed to Kenan Kaygisiz.
In this paper, we define normal soft int-groups and derive their some basic properties. We also investigate some relations on α-inclusion, soft product and normal soft int-groups. Then we define normalizer, quotient group and give some theorems concerning these concepts.
In this paper, we define k-generalized order-k numbers and we obtain a relation between i-th sequences and k-th sequences of k-generalized order-k numbers. We give some determinantal and permanental representations of k-generalized order-k numbers by using various matrices. Using the relation between i-th sequences and k-th sequences of k-generalized order-k numbers we give some determinantal and permanental representations of i-th sequences of generalized order-k numbers. In addition, we obtain Binet's formula for generalized order-k Pell numbers by using our representations.
In this paper, we present k sequences of Generalized Van der Laan Polynomials and Generalized Perrin Polynomials using Genaralized Fibonacci and Lucas Polynomials. We give some properties of these polynomials. We also obtain generalized order-k Van der Laan Numbers, k sequences of generalized order-k Van der Laan Numbers, generalized order-k Perrin Numbers and k sequences of generalized order-k Perrin Numbers. In addition, we examine the relationship between them.
In this paper, we give some determinantal and permanental representations of Generalized Fibonacci Polynomials by using various Hessenberg matrices. These results are general form of determinantal and permanental representations of k sequences of the generalized order-k Fibonacci and Pell numbers.
In this paper, we give some determinantal and permanental representations of Generalized Lucas Polynomials by using various Hessenberg matrices, which are general form of determinantal and permanental representations of ordinary Lucas and Perrin sequences. Then we show, under what conditions that the determinants of the Hessenberg matrix becomes its permanents.
In this paper, we give some determinantal and permanental representations of generalized bivariate Fibonacci p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Fibonacci p-polynomials are general form of, for example, bivariate Fibonacci and Pell p-polynomials, second kind Chebyshev polynomials, bivariate Jacobsthal polynomials etc.
In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas numbers and generalized order-k Fibonacci numbers. In addition, we obtain Binet formula and combinatorial representation for generalized order-k Lucas numbers by using properties of generalized Fibonacci numbers.