combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in

= \

O\big(\big).

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 'N'' and so

2^

subset In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset o ...

s of odd numbers in 'N'' The Cameron–Erdős conjecture says that this counts a constant proportion of the sum-free sets. The

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1 ...

was stated by Peter Cameron and Paul Erdős in 1988. It was proved by Ben Green and independently by Alexander Sapozhenko. in 2003.

Notes

Additive number theory Combinatorics Theorems in discrete mathematics Paul Erdős Conjectures that have been proved {{combin-stub

See also

Notes