Title of article :
THE COMPLEX-TYPE CYCLIC-FIBONACCI SEQUENCE AND ITS APPLICATIONS
Author/Authors :
Deveci ، Ömür Department of Mathematics - Kafkas University , Erdağ ، Özgür Department of Mathematics - Kafkas University , Güngoz ، Uğur Department of Mathematics - Kafkas University
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 cyclicFibonacci 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 D2, D3, D4, D5, D6 and D8 with respect to their generating sets.
Keywords :
he complex , type cyclic , Fibonacci sequence , Matrix , Group , Period
Journal title :
Journal of Mahani Mathematical Research Center
Journal title :
Journal of Mahani Mathematical Research Center
