Proceedings of the American Mathematical Society

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

 

 

Asymptotic nonbases which are not subsets of maximal asymptotic nonbases


Author: Julien Hennefeld
Journal: Proc. Amer. Math. Soc. 62 (1977), 23-24
MSC: Primary 10L05
MathSciNet review: 0506141
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Abstract: Let A be a set of positive integers. If all but a finite number of the positive integers can be written as a sum of h elements of A, then A is called an asymptotic basis of order h. Otherwise, A is called an asymptotic nonbasis of order h. For each $ h \geqslant 2$, we construct an asymptotic nonbasis of order h which is not a subset of a maximal asymptotic nonbasis of order h.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0506141-X
Keywords: Sum sets, asymptotic bases, asymptotic nonbases, maximal nonbases
Article copyright: © Copyright 1977 American Mathematical Society