# The Fibonacci–Circulant Sequences and Their Applications

@article{Deveci2017TheFS,
title={The Fibonacci–Circulant Sequences and Their Applications},
author={{\"O}m{\"u}r Deveci and Erdal Karaduman and Colin M. Campbell},
journal={Iranian Journal of Science and Technology, Transactions A: Science},
year={2017},
volume={41},
pages={1033-1038}
}
• Published 1 November 2017
• Mathematics
• Iranian Journal of Science and Technology, Transactions A: Science
In this paper, we define the recurrence sequences using the Circulant matrices which are obtained from the characteristic polynomial of the Fibonacci sequence, and then, we give miscellaneous properties of these sequences. In addition, we consider the cyclic groups which are generated by the generating matrices and the auxiliary equations of the defined recurrence sequences, and then, we study the orders of these cyclic groups. Furthermore, we extend the defined sequences to groups. Finally, we…
5 Citations
The complex-type k-Fibonacci sequences and their applications
• Mathematics
• 2020
Abstract In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain
On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications
• Mathematics
Communications in Algebra
• 2019
Abstract We define the Gauss Fibonacci polynomials. Then we give a formula for the Gauss Fibonacci polynomials by using the Fibonacci polynomials. The Gauss Lucas polynomials are described and the
Explicit Euclidean Norm, Eigenvalues, Spectral Norm and Determinant of Circulant Matrix with the Generalized Tribonacci Numbers
In this paper, we obtain explicit Euclidean norm, eigenvalues, spectral norm and determinant of circulant matrix with the generalized Tribonacci (generalized (r, s, t)) numbers. We also present the
The Representations of the Fibonacci and Lucas Matrices
• Fikri Koken
• Mathematics
Iranian Journal of Science and Technology, Transactions A: Science
• 2019
In this study, a matrix $$R_{L}$$RL is defined by the properties associated with the Pascal matrix, and two closed-form expressions of the matrix function $$f(R_{L})=R_{L}^{n}$$f(RL)=RLn are