On the maximum size of a (k, l)-sum-free subset of an abelian group
نویسنده
چکیده
A subset A of a given finite abelian group G is called (k, l)-sum-free if the sum of k (not necessarily distinct) elements of A does not equal the sum of l (not necessarily distinct) elements of A. We are interested in finding the maximum size λk,l(G) of a (k, l)-sum-free subset in G. A (2, 1)-sum-free set is simply called a sum-free set. The maximum size of a sum-free set in the cyclic group Zn was found almost forty years ago by Diamanda and Yap; the general case for arbitrary finite abelian groups was recently settled by Green and Ruzsa. Here we find the value of λ3,1(Zn). More generally, a recent paper of Hamidoune and Plagne examines (k, l)-sum-free sets in G when k− l and the order of G are relatively prime; we extend their results to see what happens without this assumption. 2000 Mathematics Subject Classification: Primary: 11P70; Secondary: 05D99, 11B25, 11B75, 20K01.
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