Cameron–Erdős conjecture

Template:Short description In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in $[N]=\{1,\dots ,N\}$ is $O\left(2^{N/2}\right).$

The sum of two odd numbers is even, so a set of odd numbers is always sum-free. There are $\lceil N/2\rceil$ odd numbers in [NTemplate:Hairsp], and so $2^{N/2}$ subsets of odd numbers in [NTemplate:Hairsp]. 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. It was proved by Ben Green and independently by Alexander Sapozhenko in 2003.

See also

• Erdős conjecture