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arXiv · 2609.08706

On a problem of Erd\H{o}s and Nathanson related to minimal asymptotic bases of order $h$

Shi-Qiang Chen·Quan-Hui Yang
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Abstract

Let $h\geq 3$ be an integer and $0<\alpha<1/h$. In this paper, we prove that there exists a minimal asymptotic basis of order $h$ with asymptotic density $\alpha$. This solves an open problem posed by Erd\H{o}s and Nathanson in 1988.

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Shi-Qiang Chen, Quan-Hui Yang. 2026-09-08. On a problem of Erd\H{o}s and Nathanson related to minimal asymptotic bases of order $h$. https://arxiv.org/abs/2609.08706

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