The complex-type cyclic-Fibonacci sequence and its applications
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 t...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2023-05-01
|
| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_3456_c0f2204bd9ab96b54dfe10e1b9e3ffe4.pdf |
| _version_ | 1827920792525996032 |
|---|---|
| author | Ömür Deveci Özgür Erdağ Uğur Güngoz |
| author_facet | Ömür Deveci Özgür Erdağ Uğur Güngoz |
| author_sort | Ömür Deveci |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T04:16:47Z |
| format | Article |
| id | doaj.art-882c08fd203d4758a8143de4ec42c769 |
| institution | Directory Open Access Journal |
| issn | 2251-7952 2645-4505 |
| language | English |
| last_indexed | 2024-03-13T04:16:47Z |
| publishDate | 2023-05-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj.art-882c08fd203d4758a8143de4ec42c7692023-06-21T03:19:52ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052023-05-0112223524610.22103/jmmr.2022.19786.12923456The complex-type cyclic-Fibonacci sequence and its applicationsÖmür Deveci0Özgür Erdağ1Uğur Güngoz2Department of Mathematics, Kafkas University, Kars, TurkeyDepartment of Mathematics, Kafkas University, Kars, TurkeyDepartment of Mathematics, Kafkas University, Kars, TurkeyIn 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.https://jmmrc.uk.ac.ir/article_3456_c0f2204bd9ab96b54dfe10e1b9e3ffe4.pdfthe complex-type cyclic-fibonacci sequencematrixgroupperiod |
| spellingShingle | Ömür Deveci Özgür Erdağ Uğur Güngoz The complex-type cyclic-Fibonacci sequence and its applications Journal of Mahani Mathematical Research the complex-type cyclic-fibonacci sequence matrix group period |
| title | The complex-type cyclic-Fibonacci sequence and its applications |
| title_full | The complex-type cyclic-Fibonacci sequence and its applications |
| title_fullStr | The complex-type cyclic-Fibonacci sequence and its applications |
| title_full_unstemmed | The complex-type cyclic-Fibonacci sequence and its applications |
| title_short | The complex-type cyclic-Fibonacci sequence and its applications |
| title_sort | complex type cyclic fibonacci sequence and its applications |
| topic | the complex-type cyclic-fibonacci sequence matrix group period |
| url | https://jmmrc.uk.ac.ir/article_3456_c0f2204bd9ab96b54dfe10e1b9e3ffe4.pdf |
| work_keys_str_mv | AT omurdeveci thecomplextypecyclicfibonaccisequenceanditsapplications AT ozgurerdag thecomplextypecyclicfibonaccisequenceanditsapplications AT ugurgungoz thecomplextypecyclicfibonaccisequenceanditsapplications AT omurdeveci complextypecyclicfibonaccisequenceanditsapplications AT ozgurerdag complextypecyclicfibonaccisequenceanditsapplications AT ugurgungoz complextypecyclicfibonaccisequenceanditsapplications |