Английская Википедия:Cameron–Erdős conjecture
Материал из Онлайн справочника
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
