On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix

Yasemin Taşyurdu; Zülküf Dilmen

doi:10.18466/cbayarfbe.302663

EN

On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix

Abstract

In this study, Fibonacci sequence was defined over an arbitrary ring and its some properties are investigated. The terms of this sequence are derivated by Tridiagonal determinant of the matrix. It was shown that this sequence is periodic and their period is obtained. It was shown that the sequence obtained by reducing modulo coefficient and exponent of each Fibonacci sequence in arbitrary rings is periodic. It was seen that order of cyclic group generated with matrix is equal to the period of this sequence where are arbitrary elements of the ring. Also, the period of this sequence is compared with Wall number of Fibonacci sequence and it was shown that this period always was an even number.

Keywords

Fibonacci Sequence,Finite Ring,Period

References

Taşyurdu, Y.; Gültekin, İ., The Period of Fibonacci Sequences Over The Finite Field of Order p^2, New Trends in Mathematical Sciences. 2016; 4, 248-255.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Yasemin Taşyurdu

Zülküf Dilmen This is me

Publication Date

March 30, 2017

Submission Date

March 30, 2017

Acceptance Date

-

Published in Issue

Year 2017 Volume: 13 Number: 1

DOI

https://doi.org/10.18466/cbayarfbe.302663

IZ

https://izlik.org/JA89XC48EY

Cite

RIS / Bibtex

APA

Taşyurdu, Y., & Dilmen, Z. (2017). On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. Celal Bayar University Journal of Science, 13(1), 165-169. https://doi.org/10.18466/cbayarfbe.302663

AMA

1.Taşyurdu Y, Dilmen Z. On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. CBUJOS. 2017;13(1):165-169. doi:10.18466/cbayarfbe.302663

Chicago

Taşyurdu, Yasemin, and Zülküf Dilmen. 2017. “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”. Celal Bayar University Journal of Science 13 (1): 165-69. https://doi.org/10.18466/cbayarfbe.302663.

EndNote

Taşyurdu Y, Dilmen Z (March 1, 2017) On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. Celal Bayar University Journal of Science 13 1 165–169.

IEEE

[1]Y. Taşyurdu and Z. Dilmen, “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”, CBUJOS, vol. 13, no. 1, pp. 165–169, Mar. 2017, doi: 10.18466/cbayarfbe.302663.

ISNAD

Taşyurdu, Yasemin - Dilmen, Zülküf. “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”. Celal Bayar University Journal of Science 13/1 (March 1, 2017): 165-169. https://doi.org/10.18466/cbayarfbe.302663.

JAMA

1.Taşyurdu Y, Dilmen Z. On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. CBUJOS. 2017;13:165–169.

MLA

Taşyurdu, Yasemin, and Zülküf Dilmen. “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”. Celal Bayar University Journal of Science, vol. 13, no. 1, Mar. 2017, pp. 165-9, doi:10.18466/cbayarfbe.302663.

Vancouver

1.Yasemin Taşyurdu, Zülküf Dilmen. On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. CBUJOS. 2017 Mar. 1;13(1):165-9. doi:10.18466/cbayarfbe.302663