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

DOI:
https://doi.org/10.1090/S0002-9947-1975-0376594-1

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 denote the largest quantity so that every sequence of *n* distinct integers has a sum-free subsequence consisting of integers. In this paper we strengthen previous results by Erdös, Choi and Cantor by proving

**[1]**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****[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**0313216**, https://doi.org/10.1090/S0002-9939-1973-0313216-3**[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**0325563**, https://doi.org/10.1090/S0002-9939-1973-0325563-X**[5]**V. Chvátal and J. Komlós,*Some combinatorial theorems on monotonicity*, Canad. Math. Bull.**14**(1971), 151–157. MR**0337676**, https://doi.org/10.4153/CMB-1971-028-8

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0376594-1

Keywords:
Sum-free,
subsequence,
integers

Article copyright:
© Copyright 1975
American Mathematical Society