The lowest-degree polynomials with non-negative coefficients

2012/10/25 by Tomáš Kepka, Kepka, Tomáš, Miroslav Korbelář +1
Mathematics · #13P25 #65K05 #Analytic Number Theory Research #Commutative Algebra (math.AC) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Optimization and Control (math.OC) #math.AC #math.OC #msc:13P25 #msc:65K05

paper · pdf · doi:10.48550/arxiv.1210.6868

10 pages

arxiv created 2012/10/25 · openalex publication_date 2012/10/25 · arxiv updated 2012/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A polynomial p∈ℝ[x] is a divisor of some polynomial 0≠ f∈ℝ[x] with non-negative coefficients if and only if p does not have a positive real root. The lowest possible degree of such f for a given p is known for quadratic polynomials. We provide it for cubic polynomials and improve known bounds of this value for a general polynomial.

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