The k-nacci sequences in some special modular groups

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Abstract

A k-nacci (k-step Fibonacci) sequence in a finite group is a sequence of group elements x0, x1, x2, …, xn, … for which, given an initial (seed) set x0, x1, x2, …, xj-1, each element is defined by

From the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2, …, xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups 픐2, and ℜ2, where each term of the sequence is reduced modulo 2.

Original languageEnglish
Pages (from-to)17-30
JournalAlgebra Colloquium
Volume21
Issue number59
DOIs
Publication statusPublished - 2014

Keywords

  • k-nacci sequence
  • period
  • modular group

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