关于外行排列的简短说明

Pub Date : 2022-12-01 DOI:10.2478/ausm-2022-0015

P. Hajnal

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引用次数: 0

摘要

[k] ={1,2,3，…，k}的排列p称为Layman置换，如果i + p(i)是1≤i≤k的斐波那契数，这个概念是由Layman在《整数序列百科全书》的A097082条目中引入的，即[n]的Layman置换个数。在本文中，我们将研究外行人排列。我们引入了自然数的斐波那契补的概念，它在我们的研究中起着至关重要的作用。利用这一概念，我们证明了关于Layman排列数目的一些结果，这些结果与隐含在OEIS的A097083条目中的Layman猜想有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A short note on Layman permutations

Abstract A permutation p of [k] = {1, 2, 3, …, k} is called Layman permutation iff i + p(i) is a Fibonacci number for 1 ≤ i ≤ k. This concept is introduced by Layman in the A097082 entry of the Encyclopedia of Integers Sequences, that is the number of Layman permutations of [n]. In this paper, we will study Layman permutations. We introduce the notion of the Fibonacci complement of a natural number, that plays a crucial role in our investigation. Using this notion we prove some results on the number of Layman permutations, related to a conjecture of Layman that is implicit in the A097083 entry of OEIS.

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