Английская Википедия:Cameron–Erdős conjecture

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In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in <math>[N] = \{1,\ldots,N\}</math> is <math>O\big({2^{N/2}}\big).</math>

The sum of two odd numbers is even, so a set of odd numbers is always sum-free. There are <math>\lceil N/2\rceil</math> odd numbers in [N ], and so <math>2^{N/2}</math> subsets of odd numbers in [N ]. The Cameron–Erdős conjecture says that this counts a constant proportion of the sum-free sets.

The conjecture was stated by Peter Cameron and Paul Erdős in 1988.[1] It was proved by Ben Green[2] and independently by Alexander Sapozhenko[3][4] in 2003.

See also

Notes

Шаблон:Reflist

Шаблон:Combin-stub