Bericht 00-37 des Mathematischen Seminars Kiel

00-37

Berichtsreihe des Mathematischen Seminars der Universität Kiel

Tomasz Schoen:

The Number of (2,3)-Sum-Free Subsets of {1,...,n}

A subset A of a group G is sum-free if the equation x+y=z has no solutions in A. Denote by SF(G) and SF(n) the family of all sum-free subsets of G and of the integers {1,...,n}, respectively. A well-known conjecture of Cameron and Erdös states that ¦ SF(n) ¦ = O( 2^n/2). For given positive integers k > l call a subset A of {1,...,n} (k,l)-sum-free if there are no solutions to the equation x₁+...+x_k = y₁+...+y_l in A. Denote by SF_k(n) the family of all (k+1,k)-sum-free subsets of {1,...,n}. As a step towards the conjecture of Cameron and Erdös we prove a conjecture of Bilu by showing ¦ SF₂(n) ¦ = 2^n/2 + O(2^n/2-cn), where c is an absolute positive constant.

Mathematics Subject Classification (1991): 11B75, 11A99

Tomasz Schoen:

The Number of (2,3)-Sum-Free Subsets of {1,...,n}

Mail an Jens Burmeister

[Thu Feb 19 18:56:35 2009]

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