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The Fibonacci–Circulant Sequences and Their Applications

Authors
  • Deveci, Ömür1
  • Karaduman, Erdal2
  • Campbell, Colin M.3
  • 1 Kafkas University, Department of Mathematics, Faculty of Science and Letters, Kars, 36100, Turkey , Kars (Turkey)
  • 2 Atatürk University, Department of Mathematics, Faculty of Science, Erzurum, 25240, Turkey , Erzurum (Turkey)
  • 3 University of St Andrews, North Haugh, School of Mathematics and Statistics, St Andrews, Fife, KY16 9SS, Scotland, UK , St Andrews, Fife (United Kingdom)
Type
Published Article
Journal
Iranian Journal of Science and Technology Transactions A Science
Publisher
Springer-Verlag
Publication Date
Nov 01, 2017
Volume
41
Issue
4
Pages
1033–1038
Identifiers
DOI: 10.1007/s40995-017-0317-7
Source
Springer Nature
Keywords
License
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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.

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