The Fibonacci-circulant sequences in the binary polyhedral groups

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Atatürk University, 25240, Erzurum, TURKEY

2 Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100, Kars, TURKEY

Abstract

In 2017 Deveci et al‎. ‎defined the Fibonacci-circulant sequences of the first and second kinds as shown‎, ‎respectively:‎
x_n^1 = -x_(n-1)^1+x_(n-2)^1-x_(n-3)^1 for n≥4,where x_1^1=x_2^1=0 and x_3^1=1
and
x_n^2 = -x_(n-3)^2-x_(n-4)^2+x_(n-5)^2 for n≥6,where x_1^2=x_2^2=x_3^2=x_4^2=0 and x_5^2=1
‎Also‎, ‎they extended the Fibonacci-circulant sequences of the first and second kinds to groups‎. ‎In this paper‎, ‎we obtain the periods of the Fibonacci-circulant sequences of the first and second kinds in the binary polyhedral groups‎.

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