The Fibonacci-Circulant Sequences and Their Applications

DEVECİ Ö., KARADUMAN E., Campbell C. M.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, cilt.41, ss.1033-1038, 2017 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s40995-017-0317-7
  • Dergi Adı: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1033-1038
  • Anahtar Kelimeler: Circulant matrix, Sequence, Group, Auxiliary equation, Length, FINITE-GROUPS, PADOVAN SEQUENCES, JACOBSTHAL, MATRICES, NUMBERS
  • Atatürk Üniversitesi Adresli: Evet

Özet

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.