A note on sum-free sets of integers

Hu, Mên Ch’ang

doi:10.1090/S0002-9939-1980-0587962-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A note on sum-free sets of integers
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by Mên Ch’ang Hu PDF

Proc. Amer. Math. Soc. 80 (1980), 711-712 Request permission

Abstract:

A set S of integers is said to be sum-free if $a,b \in S$ implies $a + b \notin S$. Let $g(n,k)$ denote the cardinality of a largest subset of $\{ 1,2, \ldots ,n\}$ that can be partitioned into k sum-free sets. In this note we show that $g(n,2) = n - [n/5]$.

References

H. L. Abbott and E. T. H. Wang, Sum-free sets of integers, Proc. Amer. Math. Soc. 67 (1977), no. 1, 11–16. MR 485759, DOI 10.1090/S0002-9939-1977-0485759-7