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

Author: S. L. G. Choi
Journal: Proc. Amer. Math. Soc. 39 (1973), 42-44
MSC: Primary 10L99
MathSciNet review: 0313216
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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.

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  • [1] P. Erdös, Extremal problems in number theory, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, R.I., 1965, pp. 181-189. MR 30 #4740. MR 0174539 (30:4740)

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Keywords: Sum-free, subsequence, real numbers
Article copyright: © Copyright 1973 American Mathematical Society

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