Abstract
Let N denote the set of all nonnegative integers and A be a subset of N. Let h be an integer with h≥2. Let n∈N and rh(A,n)=♯{(a1,…,ah)∈Ah:a1+⋯+ah=n}. The set A is called an asymptotic basis of order h if rh(A,n)≥1 for all sufficiently large integer n. An asymptotic basis A of order h is minimal if no proper subset of A is an asymptotic basis of order h. In 1988, Nathanson posed a problem on minimal asymptotic bases of order h. Recently, Chen and Tang showed that the answer to the problem is negative for h≥4 by constructing a special partition of N. In this paper, we give a new construction of minimal asymptotic bases. This construction expands our understanding on the problem of Nathanson.
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