The complex-type cyclic-Fibonacci sequence and its applications

Document Type : Research Paper

Authors

Department of Mathematics, Kafkas University, Kars, Turkey

Abstract

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.

Keywords

References

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History

  • Receive Date: 27 June 2022
  • Revise Date: 21 September 2022
  • Accept Date: 30 September 2022

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