论文标题
Wythoff序列，斐波那契表示及以后的总和
Sumsets of Wythoff Sequences, Fibonacci Representation, and Beyond
论文作者
论文摘要
令$α=（1+ \ sqrt {5}）/2 $，然后通过$ a_i = \ lflooriα\ rfloor $，$ b_i = \ lflooriα^2 \ rfloor $ for $ i \ geq 1 $。在最近有趣的论文中，Kawsumarng等人。证明了有关数字的许多结果，可表示为$ a_i + a_j $，$ b_i + b_j $，$ a_i + b_j $的总和。在本文中，我使用一个简单的想法和称为核桃的现有免费软件来展示如何得出所有结果。关键的想法是，对于每个总和，有一个相对较小的自动机接受所代表的数字的斐波那契表示。我还展示了自动机方法如何轻松证明其他结果。
Let $α= (1+\sqrt{5})/2$ and define the lower and upper Wythoff sequences by $a_i = \lfloor i α\rfloor$, $b_i = \lfloor i α^2 \rfloor$ for $i \geq 1$. In a recent interesting paper, Kawsumarng et al. proved a number of results about numbers representable as sums of the form $a_i + a_j$, $b_i + b_j$, $a_i + b_j$, and so forth. In this paper I show how to derive all of their results, using one simple idea and existing free software called Walnut. The key idea is that for each of their sumsets, there is a relatively small automaton accepting the Fibonacci representation of the numbers represented. I also show how the automaton approach can easily prove other results.
