In
combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of
sum-free set In additive combinatorics and number theory, a subset ''A'' of an abelian group ''G'' is said to be sum-free if the sumset ''A'' + ''A'' is disjoint from ''A''. In other words, ''A'' is sum-free if the equation a + b = c has no solution with a,b, ...
s contained in
is
The sum of two
odd
Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric.
Odd may also refer to:
Acronym
* ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...
numbers is
even
Even may refer to:
General
* Even (given name), a Norwegian male personal name
* Even (surname)
* Even (people), an ethnic group from Siberia and Russian Far East
** Even language, a language spoken by the Evens
* Odd and Even, a solitaire game w ...
, so a set of odd numbers is always sum-free. There are
odd numbers in
'N'' and so
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.
See also
*
Erdős conjecture
Erdős, Erdos, or Erdoes is a Hungarian surname.
People with the surname include:
* Ágnes Erdős (born 1950), Hungarian politician
* Brad Erdos (born 1990), Canadian football player
* Éva Erdős (born 1964), Hungarian handball player
* Józ ...
Notes
Additive number theory
Combinatorics
Theorems in discrete mathematics
Paul Erdős
Conjectures that have been proved
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