On a problem of Erdős and Nathanson related to minimal asymptotic bases of order $h$

Abstract

Let $h\ge 3$ 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 Erdős and Nathanson in 1988.

10 pages