On the maximum density of minimal asymptotic bases
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- by Melvyn B. Nathanson and András Sárközy PDF
- Proc. Amer. Math. Soc. 105 (1989), 31-33 Request permission
Abstract:
A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer is the sum of $h$ elements of $A$. It is proved that if $A$ is an asymptotic basis of order $h$ with lower asymptotic density ${d_L}(A) > 1/h$, then there is a set $W$ contained in $A$ such that $W$ has positive asymptotic density and $A\backslash W$ is an asymptotic basis of order $h$. This implies that if $A$ is a minimal asymptotic basis of order $h$, then ${d_L}(A) \leq 1/h$.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 31-33
- MSC: Primary 11B13; Secondary 11B05, 11P99
- DOI: https://doi.org/10.1090/S0002-9939-1989-0973836-1
- MathSciNet review: 973836