Cameron–Erdős conjecture
From Wikipedia, the free encyclopedia
In combinatorics, the Cameron–Erdős conjecture 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 2N / 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.[1] It was proved by Ben Green[2] and independently by Alexander Sapozhenko[3][4] in 2003.
[edit] See also
[edit] Notes
- ^ Cameron, P. J.; Erdős, P. (1990), "On the number of sets of integers with various properties", Number theory: proceedings of the First Conference of the Canadian Number Theory Association, held at the Banff Center, Banff, Alberta, April 17-27, 1988, Berlin: de Gruyter, pp. 61–79, MR1106651, http://books.google.com/books?id=68g0Ds4FNM0C&pg=PA61&lpg=PA61.
- ^ Green, Ben (2004), "The Cameron-Erdős conjecture", The Bulletin of the London Mathematical Society 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR2083752.
- ^ Sapozhenko, A. A. (2003), "The Cameron-Erdős conjecture", Doklady Akademii Nauk 393 (6): 749–752, MR2088503.
- ^ Sapozhenko, Alexander A. (2008), "The Cameron-Erdős conjecture", Discrete Mathematics 308 (19): 4361–4369, doi:10.1016/j.disc.2007.08.103, MR2433862.
.svg){kind=small} |
This combinatorics-related article is a stub. You can help Wikipedia by expanding it. |
