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Nazmiye Yilmaz

Publications and source records attributed to Nazmiye Yilmaz.

10 recordsLinked to original sources
arXiv2016

A note on the bi-periodic Fibonacci and Lucas matrix sequences

In this paper, we introduce the bi-periodic Lucas matrix sequence and present some fundamental properties of this generalized matrix sequence. Moreover, we investigate the important relationships between the bi-periodic Fibonacci and Lucas matrix sequences. We express that some behaviours of bi-periodic Lucas numbers also can be obtained by considering properties of this new matrix sequence. Finally, we say that the matrix sequences as Lucas, $k$-Lucas and Pell-Lucas are special cases of this generalized matrix sequence.

math.NT↗
arXiv2016

The Bi-periodic Fibonacci Octonions

In this paper, by using bi-periodic Fibonacci numbers, we introduce the bi-periodic Fibonacci octonions. After that, we derive the generating function of these octonions as well as investigated some properties over them. Also, as another main result of this paper, we give the summations for bi-periodic Fibonacci octonions.

math.NT↗
arXiv2016

Bi-periodic incomplete Lucas numbers

In this paper, by presenting bi-periodic Lucas numbers as a binomial sum, we introduce the bi-periodic incomplete Lucas numbers. After that, by using the bi-periodic incomplete Lucas numbers, we derive the recurrence relation and the generating function of these numbers as well as investigated some properties over them. Additionally, as another main result of this paper, we give some relations between bi-periodic incomplete Lucas numbers and bi-periodic incomplete Fibonacci numbers.

math.NT↗
arXiv2016

The Binomial Transforms of Tribonacci and Tribonacci-Lucas sequences

In this study, we apply the binomial transforms to Tribonacci and Tribonacci-Lucas sequences. Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we illustrate the relation between these transforms by deriving new formulas.

math.CO↗
arXiv2016

On the g-Circulant Matrix involving the Generalized k-Horadam Numbers

In this study, we present a new generalization of circulant matrices for the generalized $k$-Horadam numbers, by considering the $g$-circulant matrix $C_{n,g}(H)=g -circ(H_{k,1},H_{k,2},\ldots ,H_{k,n})$. Also, we calculate the spectral norm, determinant and inverse of $C_{n,g}(H)$ in such matrices having the elements of all second order sequences.

math.NT↗
arXiv2015

Iterated binomial transform of the k-Lucas sequence

In this study, we apply "r" times the binomial transform to k-Lucas sequence. Also, the Binet formula, summation, generating function of this transform are found using recurrence relation. Finally, we give the properties of iterated binomial transform with classical Lucas sequence.

math.NT↗
arXiv2014

On the binomial sums of Horadam sequence

The main purpose of this paper is to establish some new properties of Horadam numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between Horadam and generalized Lucas numbers are revealed to get a more strong result.

math.CO↗
arXiv2014

On properties of Tribonacci-Lucas polynomials

In this paper, we investigated properties of Tribonacci-Lucas polynomials which generalized Tribonacci-Lucas numbers. From this generalization, we also obtain some new algebraic properties on these numbers and polynomials as Binet formula, summation, binomial sum and generating function.

math.NT↗