Maximal sum-free sets in finite abelian groups
نویسندگان
چکیده
منابع مشابه
Sum-free Sets in Abelian Groups
Let A be a subset of an abelian group G with |G| = n. We say that A is sum-free if there do not exist x, y, z ∈ A with x+ y = z. We determine, for any G, the maximal density μ(G) of a sum-free subset of G. This was previously known only for certain G. We prove that the number of sum-free subsets of G is 2, which is tight up to the o-term. For certain groups, those with a small prime factor of t...
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Let A be a subset of a finite abelian group G. We say that A is sum-free if the equation x + y = z, has no solution (x, y, z) with x, y, z belonging to the set A. In this paper we shall characterise the largest possible sum-free subsets of G in case the order of G is only divisible by primes which are congruent to 1 modulo 3.
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Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x+ y = z, with x, y, z belonging to the set A. Let SF (G) the sel of all sum-free subets of G and σ(G) deonotes the number n(log 2 |SF (G)|). In this article we shall improve the error term in asymptotic formula of σ(G) obtained in [GR05]. The methods used are a slight refinement of ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1970
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270004199x