论文标题
Zeckendorf扩展的结构
The structure of Zeckendorf expansions
论文作者
论文摘要
在本文中，我们根据其数字块对Zeckendorf扩展进行了分类。事实证明，如果我们将这些数字块视为斐波那契树上的标签，那么在其Zeckendorf扩展中以给定的数字块结尾的数字以自然方式以自然的方式显示为复合Wythoff序列。在这里，仅由$ 0 $组成的数字块是一个例外。我们还将这些出现序列作为广义的比蒂序列提供了第二个描述。最后，我们以固定数字块在其zeckendorf扩展中的任意固定位置出现的数字表征，并确定其密度。
In this paper we classify the Zeckendorf expansions according to their digit blocks. It turns out that if we consider these digit blocks as labels on the Fibonacci tree, then the numbers ending with a given digit block in their Zeckendorf expansion appear as compound Wythoff sequences in a natural way on this tree. Here the digit blocks consisting of only $0$'s are an exception. We also give a second description of these occurrence sequences as generalized Beatty sequences. Finally, we characterize the numbers with a fixed digit block occurring at an arbitrary fixed position in their Zeckendorf expansions, and determine their densities.
