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Transactions of the American Mathematical Society

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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}}.$

References [Enhancements On Off] (What's this?)

  • [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)
  • [2] S. L. G. Choi, The largest sum-free subsequence from a sequence of n numbers, Proc. Amer. Math. Soc. 39 (1973), 42-44. MR 47 #1771. MR 0313216 (47:1771)
  • [3] D. Cantor (to appear).
  • [4] S. L. G. Choi, On sequences not containing a large sum-free subsequence, Proc. Amer. Math. Soc. 41 (1973), 415-418. MR 48 #3910. MR 0325563 (48:3910)
  • [5] V. Chvátal and J. Komlós, Some combinatorial theorems on monotonicity, Canad. Math. Bull. 14 (1971), 151-157. MR 0337676 (49:2445)

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Keywords: Sum-free, subsequence, integers
Article copyright: © Copyright 1975 American Mathematical Society

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