Cameron–Erdős conjecture

In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in | N | = { 1 , … , N } is O ( 2 N / 2 ) .

The sum of two odd numbers is even, so a set of odd numbers is always sum-free. There are ⌈ N / 2 ⌉ odd numbers in |N|, and so 2 N / 2 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. It was proved by Ben Green and independently by Alexander Sapozhenko in 2003.