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

, 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, a Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), 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 a ...

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 or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

was stated by

Peter Cameron Peter Cameron may refer to: * Peter Cameron (entomologist) (1847–1912), English entomologist who specialised in Hymenoptera * Peter Cameron (mathematician) (born 1947), Australian mathematician, joint winner of the 2003 Euler Medal * Peter Camero ...

and

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

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