Cameron–Erdős conjecture

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In combinatorial mathematics, the Cameron–Erdős conjecture is the statement that the number of sum-free sets contained in \{1,\ldots,N\} is O\left({2^{N/2}}\right).

The conjecture was stated by Peter Cameron and Paul Erdős in 1988.[1] It was proved by Ben Green in 2003.[2][3]

A different proof has recently been found by Sasha Sapozhenko.[4]

[edit] See also

[edit] References

  1. ^ P.J. Cameron and P. Erdős, On the number of sets of integers with various properties, Number theory (Banff, 1988), de Gruyter, Berlin 1990, pp.61-79
  2. ^ B. Green, The Cameron-Erdős conjecture, 2003.
  3. ^ B. Green, The Cameron-Erdős conjecture, Bulletin of the London Mathematical Society 36 (2004) pp.769-778
  4. ^ A. Sapozhenko, The Cameron-Erdős conjecture, Discrete Mathematics, in press
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