A characterization of polynomials whose high powers have non-negative coefficients

IF 1 3区数学 Q1 MATHEMATICS Discrete Analysis Pub Date : 2019-10-15 DOI:10.19086/DA.18560

Marcus Michelen, J. Sahasrabudhe

引用次数: 3

Abstract

Let $f \in \mathbb{R}[x]$ be a polynomial with real coefficients. We say that $f$ is eventually non-negative if $f^m$ has non-negative coefficients for all sufficiently large $m \in \mathbb{N}$. In this short note, we give a classification of all eventually non-negative polynomials. This generalizes a theorem of De Angelis, and proves a conjecture of Bergweiler, Eremenko and Sokal

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具有非负系数的高幂多项式的一个性质

设$f \in \mathbb{R}[x]$是一个实系数多项式。如果$f^m$对于所有足够大的$m \ \在\mathbb{N}$中都有非负系数，我们说$f$最终是非负的。在这个简短的笔记中，我们给出了所有最终非负多项式的分类。推广了De Angelis的一个定理，证明了Bergweiler、Eremenko和Sokal的一个猜想

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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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.

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