K-nacci Sequences in Finite Triangle Groups

Erdal Karaduman and Ömür Deveci

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-10

Abstract:

A k - nacci sequence in a finite group is a sequence of group elements x 0 , x 1 , x 2 , … , x n , … for which, given an initial (seed) set x 0 , x 1 , x 2 , … , x j − 1 , each element is defined by x n = x 0 x 1 … x n − 1 , for j ≤ n < k, and x n = x n − k x n − k + 1 … x n − 1 , for n ≥ k . We also require that the initial elements of the sequence, x 0 , x 1 , x 2 , … , x j − 1 , generate the group, thus forcing the k -nacci sequence to reflect the structure of the group. The K-nacci sequence of a group generated by x 0 , x 1 , x 2 , … , x j − 1 is denoted by F k ( G ; x 0 , x 1 , … , x j − 1 ) and its period is denoted by P k ( G ; x 0 , x 1 , … , x j − 1 ) . In this paper, we obtain the period of K-nacci sequences in finite polyhedral groups and the extended triangle groups.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:453750

DOI: 10.1155/2009/453750

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