Maximal asymptotic nonbases
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- by Paul Erdős and Melvyn B. Nathanson PDF
- Proc. Amer. Math. Soc. 48 (1975), 57-60 Request permission
Abstract:
Let $A$ be a set of nonnegative integers. If all but a finite number of positive integers can be written as a sum of $h$ elements of $A$, then $A$ is an asymptotic basis of order $h$. Otherwise, $A$ is an asymptotic nonbasis of order $h$. A class of maximal asymptotic nonbases is constructed, and it is proved that any asymptotic nonbasis of order 2 that satisfies a certain finiteness condition is a subset of a maximal asymptotic nonbasis of order 2.References
- Melvyn B. Nathanson, Minimal bases and maximal nonbases in additive number theory, J. Number Theory 6 (1974), 324–333. MR 347764, DOI 10.1016/0022-314X(74)90028-6
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 57-60
- DOI: https://doi.org/10.1090/S0002-9939-1975-0357363-0
- MathSciNet review: 0357363