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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On sum-free subsequences


Authors: S. L. G. Choi, J. Komlós and E. Szemerédi
Journal: Trans. Amer. Math. Soc. 212 (1975), 307-313
MSC: Primary 10L05
MathSciNet review: 0376594
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Abstract: A subsequence of a sequence of n distinct integers is said to be sum-free if no integer in it is the sum of distinct integers in it. Let $ f(n)$ denote the largest quantity so that every sequence of n distinct integers has a sum-free subsequence consisting of $ f(n)$ integers. In this paper we strengthen previous results by Erdös, Choi and Cantor by proving

$\displaystyle {(n\;\log \;n/\log \;\log \;n)^{{\raise0.5ex\hbox{$\scriptstyle 1... ....15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} \ll f(n) \ll n{(\log \;n)^{ - 1}}.$


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0376594-1
PII: S 0002-9947(1975)0376594-1
Keywords: Sum-free, subsequence, integers
Article copyright: © Copyright 1975 American Mathematical Society