论文标题
在广义的Zeckendorf分解和广义金弦上
On Generalized Zeckendorf Decompositions and Generalized Golden Strings
论文作者
论文摘要
Zeckendorf证明，每个正整数都具有独特的表示形式，作为非连续斐波那契数的总和。该定理的自然概括是查看定义为以下的顺序：对于$ n \ ge 2 $，令$ f_ {n，1} = f_ {n，2} = \ cdots = f_ {n，n} = 1 $ and $ f_ {n，m+1} = f_ {n，m+1} = f_ {众所周知，每个正整数都具有唯一的表示形式，作为$ f_ {n，m} $的总和，其中汇总的索引至少是$ n $的。我们将其称为$ n $ dement。格里菲斯（Griffiths）在Zeckendorf分解与金弦之间展示了有趣的关系。在本文中，我们继续进行工作，以展示$ n $分解与广义金弦之间的关系。
Zeckendorf proved that every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers. A natural generalization of this theorem is to look at the sequence defined as follows: for $n\ge 2$, let $F_{n,1} = F_{n,2} = \cdots = F_{n,n} = 1$ and $F_{n, m+1} = F_{n, m} + F_{n, m+1-n}$ for all $m\ge n$. It is known that every positive integer has a unique representation as a sum of $F_{n,m}$'s where the indexes of summands are at least $n$ apart. We call this the $n$-decomposition. Griffiths showed an interesting relationship between the Zeckendorf decomposition and the golden string. In this paper, we continue the work to show a relationship between the $n$-decomposition and the generalized golden string.
