The k-Nacci Sequences in Some Special Modular Groups

• 作者: Colin M. Campbell Omur Deveci
• 来源期刊: 代数集刊:英文版
• 学科: 物理学
• 关键词: 序列 模块 斐波那契 发电机组 有限群 定义 周期
• 年，卷（期）: 2014,（1）
• 页码范围: 59-66
• 页数: 8页
• 分类号: O753.3
• 语种: 中文

摘要

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 xn{x0x1…xn-1 forj≤n〈k xn-kxn-k+1 …xn-1 for n≥kFrom 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 m2, m2+ and R2, where each term of the sequence is reduced modulo 2.