An improved lower bound for Folkman's theorem:

József Balogh, Sean Eberhard, Bhargav Narayanan, Andrew Treglown, Adam Zsolt Wagner

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)745-747
Number of pages3
JournalBulletin of the London Mathematical Society
Issue number4
StatePublished - Aug 2017


  • 05D10 (primary)
  • 05D40 (secondary)

ASJC Scopus subject areas

  • General Mathematics


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