“Cameron–Erdős conjecture”的意思、由来-开放百科全书

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

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

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.

See also

Notes

1. ^{{citation | last1 = Cameron | first1 = P. J. | author1-link = Peter Cameron (mathematician) | last2 = Erdős | first2 = P. | author2-link = Paul Erdős | contribution = On the number of sets of integers with various properties | location = Berlin | mr = 1106651 | pages = 61–79 | publisher = de Gruyter | title = Number theory: proceedings of the First Conference of the Canadian Number Theory Association, held at the Banff Center, Banff, Alberta, April 17-27, 1988 | url = https://books.google.com/books?id=68g0Ds4FNM0C&pg=PA61&lpg=PA61 | year = 1990}}.
2. ^{{citation | last = Green | first = Ben | author-link = Ben J. Green | arxiv = math.NT/0304058 | doi = 10.1112/S0024609304003650 | issue = 6 | journal = The Bulletin of the London Mathematical Society | mr = 2083752 | pages = 769–778 | title = The Cameron-Erdős conjecture | volume = 36 | year = 2004}}.
3. ^{{citation | last = Sapozhenko | first = A. A. | issue = 6 | journal = Doklady Akademii Nauk | mr = 2088503 | pages = 749–752 | title = The Cameron-Erdős conjecture | volume = 393 | year = 2003}}.
4. ^{{citation | last = Sapozhenko | first = Alexander A. | doi = 10.1016/j.disc.2007.08.103 | issue = 19 | journal = Discrete Mathematics | mr = 2433862 | pages = 4361–4369 | title = The Cameron-Erdős conjecture | volume = 308 | year = 2008}}.