Cameron–Erdős conjecture: Difference between revisions

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The '''Cameron-Erdős conjecture''' in the field of [[combinatorics]] within [[mathematics]] is the statement that the number of [[sum-free set]]s contained in <math>\{1,\ldots,N\}</math> is <math>O\left({2^{N/2}}\right)</math>.
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The '''Cameron-Erdős conjecture''' in the field of [[combinatorics]] is the statement that the number of [[sum-free set]]s contained in <math>\{1,\ldots,N\}</math> is <math>O\left({2^{N/2}}\right)</math>.


The conjecture was stated by [[Peter Cameron (mathematician)|Peter Cameron]] and [[Paul Erdős]] in 1988<ref>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</ref>.  It was proved by [[Ben Green]] in 2003<ref>B. Green, [http://www.arxiv.org/pdf/math.NT/0304058 The Cameron-Erdős conjecture], 2003.</ref> <ref>B. Green, ''The Cameron-Erdős conjecture'', Bulletin of the [[London Mathematical Society]] '''36''' (2004) pp.769-778</ref>.
The conjecture was stated by [[Peter Cameron (mathematician)|Peter Cameron]] and [[Paul Erdős]] in 1988<ref>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</ref>.  It was proved by [[Ben Green]] in 2003<ref>B. Green, [http://www.arxiv.org/pdf/math.NT/0304058 The Cameron-Erdős conjecture], 2003.</ref> <ref>B. Green, ''The Cameron-Erdős conjecture'', Bulletin of the [[London Mathematical Society]] '''36''' (2004) pp.769-778</ref>.
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The Cameron-Erdős conjecture in the field of combinatorics is the statement that the number of sum-free sets contained in is .

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

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
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