On the k-Nacci Sequences in Finite Binary Polyhedral Groups

Author:

Deveci Ömür1,Karaduman Erdal2,Campbell Colin M.3

Affiliation:

1. Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100 Kars, Turkey

2. Department of Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum, Turkey

3. School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, United Kingdom

Abstract

A k-nacci sequence in a finite group is a sequence of group elements x0,x1,…,xn,… for which, given an initial (seed) set x0,x1,…,xj-1, each element is defined by [Formula: see text] It is important to note that the Fibonacci length depends on the chosen generating n-tuple for a group. The binary polyhedral groups have been studied recently by C.M. Campbell and P.P. Campbell for their Fibonacci lengths. In this paper, we obtain the period of k-nacci sequences in the binary polyhedral groups 〈2,2,2〉, 〈n,2,2〉, 〈2,n,2〉 and 〈2,2,n〉 for any n > 2.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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