Folkman's theorem asserts that for each kϵN, there exists a natural number n=F(k) such that whenever the elements of [n] are two-coloured, there exists a set A C[n] of size k with the property that all the sums of the form σxϵBx, where B is a nonempty subset of A, are contained in [n] and have the same colour. In 1989, Erds and Spencer showed that F(k)≥2ck2/logk, where c>0 is an absolute constant; here, we improve this bound significantly by showing that F(k)≥22k-1/k for all kϵN.
|Original language||English (US)|
|Number of pages||3|
|Journal||Bulletin of the London Mathematical Society|
|State||Published - Aug 2017|
- 05D10 (primary)
- 05D40 (secondary)
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