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- W3048608217 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." @default.
- W3048608217 created "2020-08-18" @default.
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- W3048608217 date "2021-01-01" @default.
- W3048608217 modified "2023-09-25" @default.
- W3048608217 title "On a problem of Nathanson on minimal asymptotic bases" @default.
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- W3048608217 doi "https://doi.org/10.1016/j.jnt.2020.07.014" @default.
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