On the structure and the number of sum-free sets
On the structure and the number of sum-free sets
Astérisque | 1992

Anglais
A finite set A of positive integers is called sum-free if A∩(A+A)=∅. For n odd, {1,3,5,…,n} and {n+12,n+32,…,n} are examples of such sets. Denote by m and l, respectively, the largest and smallest elements of A and by a the cardinality of A. We show that if the cardinality of the sum-free set A does not differ much from l2, then A does not differ much from one of the two examples mentioned above. More precisely, if a>512l+2, then either all elements of A are odd or A contains both odd and even integers and m≥a. It is shown that if a>512l+2 then the number of such sum-free sets is O(2n/2) which proves for such sets the conjecture of P. Cameron and P. Erdös.
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