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The complex-type cyclic-Fibonacci sequence and its applications | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 235-246 اصل مقاله (547.26 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19786.1292 | ||
| نویسندگان | ||
| Ömür Deveci؛ Özgür Erdağ* ؛ Uğur Güngoz | ||
| Department of Mathematics, Kafkas University, Kars, Turkey | ||
| چکیده | ||
| In the present paper, we aim to generalize the notion of complex-type Fibonacci sequences to complex-type cyclic Fibonacci sequences. Firstly, we define the complex-type cyclic-Fibonacci sequence and then we give miscellaneous properties of this sequence by using the matrix method. Also, we study the complex-type cyclic-Fibonacci sequence modulo $m$. In addition, we describe the complex-type cyclic-Fibonacci sequence in a $2$-generator group and investigate that in finite groups in details. Then, as our last result, we obtain the lengths of the periods of the complex-type cyclic-Fibonacci sequences in dihedral groups $D_{2}$, $D_{3}$, $D_{4}$, $D_{5}$, $D_{6}$ and $D_{8}$ with respect to their generating sets. | ||
| کلیدواژه‌ها | ||
| The complex-type cyclic-Fibonacci sequence؛ Matrix؛ Group؛ Period | ||
| مراجع | ||
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