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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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