On sum-free subsequences

Choi, S. L. G.; Komlós, J.; Szemerédi, E.

doi:10.1090/S0002-9947-1975-0376594-1

On sum-free subsequences
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by S. L. G. Choi, J. Komlós and E. Szemerédi PDF

Trans. Amer. Math. Soc. 212 (1975), 307-313 Request permission

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 \[ (n \log n/\log \log n)^{1/2} \ll f(n) \ll n (\log n)^{-1}. \]

References

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