On sum-free subsequences
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- by David G. Cantor PDF
- Proc. Amer. Math. Soc. 43 (1974), 67-68 Request permission
Abstract:
A sequence of real numbers is said to be sum-free if no number of the sequence is the sum of distinct elements of the same sequence. In this paper we show that a sequence $S$ of $n$ positive real numbers has a sum-free subsequence containing at least ${(2n)^{1/2}} - {\log _2}(4n)$ elements.References
- S. L. G. Choi, The largest sum-free subsequence from a sequence of $n$ numbers, Proc. Amer. Math. Soc. 39 (1973), 42–44. MR 313216, DOI 10.1090/S0002-9939-1973-0313216-3
- 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
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 67-68
- MSC: Primary 10L10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0374078-2
- MathSciNet review: 0374078