The Fibonacci-Circulant sequences and their applications

Ömür Deveci, Erdal Karaduman, Colin M. Campbell

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1033-1038
Number of pages6
JournalIranian Journal of Science and Technology, Transactions A: Science
Volume41
Issue number4
Early online date1 Nov 2017
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Circulant matrix
  • Sequence
  • Group
  • Auxiliary equation
  • Length

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