非负矩阵幂中正项数单调性的一个备用证明

Art Discret. Appl. Math. Pub Date : 2020-08-11 DOI:10.26493/2590-9770.1280.4DA

S. Filipovski

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引用次数: 0

摘要

设A为n阶的非负实数矩阵，f(A)表示A中的正条目数。2018年，Xie证明了如果f(A)≤3或f(A)≥n2−2n + 2，则序列(f(Ak))k = 1∞对于正整数k是单调的。在本文中，我们通过计数n阶有向图中的游动来给出该结果的替代证明。

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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An alternate proof of the monotonicity of the number of positive entries in nonnegative matrix powers

Let A be a nonnegative real matrix of order n and f(A) denote the number of positive entries in A. In 2018, Xie proved that if f(A) ≤ 3 or f(A) ≥ n2 − 2n + 2, then the sequence (f(Ak))k = 1∞ is monotone for positive integers k. In this note we give an alternate proof of this result by counting walks in a digraph of order n.

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Art Discret. Appl. Math.

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