In
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
is
The sum of two
odd numbers is
even, so a set of odd numbers is always sum-free. There are
odd numbers in
'N'' and so
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.
See also
*
Erdős conjecture
Notes
Additive number theory
Combinatorics
Theorems in discrete mathematics
Paul Erdős
Conjectures that have been proved
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