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≤...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.展开更多
文摘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.
