On sequences not containing a large sum-free subsequence
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- by S. L. G. Choi
- Proc. Amer. Math. Soc. 41 (1973), 415-418
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325563-X
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Abstract:
A subsequence of a sequence of integers is said to be sum-free if no integer of the subsequence is the sum of distinct integers of this same subsequence. In this paper we shall prove, provided $n$ is sufficiently large, that there exists a sequence of $n$ integers whose largest sum-free subsequence has at most $cn{(\log \log n)^{ - 1/2}}$ integers, where $c$ is an absolute constant.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
- P. Varnavides, On certain sets of positive density, J. London Math. Soc. 34 (1959), 358–360. MR 106865, DOI 10.1112/jlms/s1-34.3.358
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 415-418
- MSC: Primary 10L05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325563-X
- MathSciNet review: 0325563