SMF

On the structure and the number of sum-free sets

On the structure and the number of sum-free sets

Gregory A. FREIMAN
On the structure and the number of sum-free sets
     
                
  • Année : 1992
  • Tome : 209
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 11B75
  • Pages : 195-201
  • DOI : 10.24033/ast.163

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 ma. 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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