The largest sum-free subsequence from a sequence of 𝑛 numbers

Choi, S. L. G.

doi:10.1090/S0002-9939-1973-0313216-3

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)

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The largest sum-free subsequence from a sequence of $n$ numbers
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by S. L. G. Choi PDF

Proc. Amer. Math. Soc. 39 (1973), 42-44 Request permission

Abstract:

Let $g(n)$ denote the largest integer so that from any sequence of $n$ real numbers one can always select a sum-free subsequence of $g(n)$ numbers. Erdös has shown that $g(n) > {2^{ - 1/2}}{n^{1/2}}$. In this paper we obtain an improved estimate by a different method.

References

P. Erdős, Extremal problems in number theory, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 181–189. MR 0174539