On sumfree subsequences
Authors:
S. L. G. Choi, J. Komlós and E. Szemerédi
Journal:
Trans. Amer. Math. Soc. 212 (1975), 307313
MSC:
Primary 10L05
MathSciNet review:
0376594
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Abstract: A subsequence of a sequence of n distinct integers is said to be sumfree 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 sumfree 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
(30 #4740)
 [2]
S.
L. G. Choi, The largest sumfree subsequence from
a sequence of 𝑛 numbers, Proc. Amer.
Math. Soc. 39
(1973), 42–44. MR 0313216
(47 #1771), http://dx.doi.org/10.1090/S00029939197303132163
 [3]
D. Cantor (to appear).
 [4]
S.
L. G. Choi, On sequences not containing a large
sumfree subsequence, Proc. Amer. Math.
Soc. 41 (1973),
415–418. MR 0325563
(48 #3910), http://dx.doi.org/10.1090/S0002993919730325563X
 [5]
V.
Chvátal and J.
Komlós, Some combinatorial theorems on monotonicity,
Canad. Math. Bull. 14 (1971), 151–157. MR 0337676
(49 #2445)
 [1]
 P. Erdös, Extremal problems in number theory, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, R. I., 1965, pp. 181189. MR 30 #4740. MR 0174539 (30:4740)
 [2]
 S. L. G. Choi, The largest sumfree subsequence from a sequence of n numbers, Proc. Amer. Math. Soc. 39 (1973), 4244. MR 47 #1771. MR 0313216 (47:1771)
 [3]
 D. Cantor (to appear).
 [4]
 S. L. G. Choi, On sequences not containing a large sumfree subsequence, Proc. Amer. Math. Soc. 41 (1973), 415418. MR 48 #3910. MR 0325563 (48:3910)
 [5]
 V. Chvátal and J. Komlós, Some combinatorial theorems on monotonicity, Canad. Math. Bull. 14 (1971), 151157. MR 0337676 (49:2445)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197503765941
PII:
S 00029947(1975)03765941
Keywords:
Sumfree,
subsequence,
integers
Article copyright:
© Copyright 1975
American Mathematical Society
