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The Fibonacci-Circulant sequences and their applications

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The Fibonacci-Circulant sequences and their applications. / Deveci, Ömür; Karaduman, Erdal; Campbell, Colin M.

In: Iranian Journal of Science and Technology, Transactions A: Science, Vol. 41, No. 4, 01.12.2017, p. 1033-1038.

Research output: Contribution to journalArticle

Harvard

Deveci, Ö, Karaduman, E & Campbell, CM 2017, 'The Fibonacci-Circulant sequences and their applications' Iranian Journal of Science and Technology, Transactions A: Science, vol. 41, no. 4, pp. 1033-1038. DOI: 10.1007/s40995-017-0317-7

APA

Deveci, Ö., Karaduman, E., & Campbell, C. M. (2017). The Fibonacci-Circulant sequences and their applications. DOI: 10.1007/s40995-017-0317-7

Vancouver

Deveci Ö, Karaduman E, Campbell CM. The Fibonacci-Circulant sequences and their applications. Iranian Journal of Science and Technology, Transactions A: Science. 2017 Dec 1;41(4):1033-1038. Available from, DOI: 10.1007/s40995-017-0317-7

Author

Deveci, Ömür ; Karaduman, Erdal ; Campbell, Colin M./ The Fibonacci-Circulant sequences and their applications. In: Iranian Journal of Science and Technology, Transactions A: Science. 2017 ; Vol. 41, No. 4. pp. 1033-1038

Bibtex - Download

@article{f105921f0e2544a4974c10bf3facb686,
title = "The Fibonacci-Circulant sequences and their applications",
abstract = "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 obtain the lengths of the periods of the extended sequences in the polyhedral groups (2, 3, 3) and (n, 2, 2) as applications of the results obtained.",
keywords = "Circulant matrix, Sequence, Group, Auxiliary equation, Length",
author = "{\"O}m{\"u}r Deveci and Erdal Karaduman and Campbell, {Colin M.}",
note = "This Project was supported by the Commission for the Scientific Research Projects of Kafkas University. The Project Number 2014-FEF-34.",
year = "2017",
month = "12",
day = "1",
doi = "10.1007/s40995-017-0317-7",
language = "English",
volume = "41",
pages = "1033--1038",
journal = "Iranian Journal of Science and Technology, Transactions A: Science",
issn = "1028-6276",
publisher = "Springer",
number = "4",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - The Fibonacci-Circulant sequences and their applications

AU - Deveci,Ömür

AU - Karaduman,Erdal

AU - Campbell,Colin M.

N1 - This Project was supported by the Commission for the Scientific Research Projects of Kafkas University. The Project Number 2014-FEF-34.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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 obtain the lengths of the periods of the extended sequences in the polyhedral groups (2, 3, 3) and (n, 2, 2) as applications of the results obtained.

AB - 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 obtain the lengths of the periods of the extended sequences in the polyhedral groups (2, 3, 3) and (n, 2, 2) as applications of the results obtained.

KW - Circulant matrix

KW - Sequence

KW - Group

KW - Auxiliary equation

KW - Length

U2 - 10.1007/s40995-017-0317-7

DO - 10.1007/s40995-017-0317-7

M3 - Article

VL - 41

SP - 1033

EP - 1038

JO - Iranian Journal of Science and Technology, Transactions A: Science

T2 - Iranian Journal of Science and Technology, Transactions A: Science

JF - Iranian Journal of Science and Technology, Transactions A: Science

SN - 1028-6276

IS - 4

ER -

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ID: 251708885