论文标题
Zeckendorf定理的微弱匡威
The weak converse of Zeckendorf's Theorem
论文作者
论文摘要
根据Zeckendorf的定理，每个正整数都是独特地写成的，是斐波那契序列的非贴种项之和，其相反的是，如果正整数中的序列具有此属性，则必须是fibonacci序列。相反，如果我们考虑找到具有这样属性的单调序列的问题，我们将其称为Zeckendorf定理的弱匡威。在本文中，我们首先介绍了Zeckendorf条件的概括，随后，Zeckendorf的定理及其对一般Zeckendorf条件的弱对话。我们还将概括和结果扩展到间隔$（0,1）$的实数，并将其扩展到$ p $ -Adic Integers。
By Zeckendorf's Theorem, every positive integer is uniquely written as a sum of non-adjacent terms of the Fibonacci sequence, and its converse states that if a sequence in the positive integers has this property, it must be the Fibonacci sequence. If we instead consider the problem of finding a monotone sequence with such a property, we call it the weak converse of Zeckendorf's theorem. In this paper, we first introduce a generalization of Zeckendorf conditions, and subsequently, Zeckendorf's theorems and their weak converses for the general Zeckendorf conditions. We also extend the generalization and results to the real numbers in the interval $(0,1)$, and to $p$-adic integers.
