The Fibonacci-Circulant Sequences and Their Applications
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.
Anahtar kelimeler
Atıf için künye
DEVECİ, Ö., Karaduman, E., & Campbell, C. M. (2017). The Fibonacci-Circulant Sequences and Their Applications. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 41, 1033–1038. https://doi.org/10.1007/s40995-017-0317-7
BibTeX
@article{deveci2017-73574,
author = {DEVECİ, ÖMÜR and Karaduman, Erdal and Campbell, Colin M.},
title = {The Fibonacci-Circulant Sequences and Their Applications},
journal = {IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE},
year = {2017},
volume = {41},
pages = {1033--1038},
issn = {1028-6276},
doi = {10.1007/s40995-017-0317-7},
url = {https://akademik.atauni.edu.tr/yayinlar/73574-the-fibonacci-circulant-sequences-and-their-applications}
}