منابع مشابه
Zero-sum free sets with small sum-set
Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.
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Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.
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Let G be a group and S a non-empty subset of G. If ab / ∈ S for any a, b ∈ S, then S is called sum-free. We show that if S is maximal by inclusion and no proper subset generates 〈S〉 then |S| ≤ 2. We determine all groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists a ∈ S such that a / ∈ 〈S \ {a}〉.
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For any C ⊆ R there is a subset A ⊆ C such that A + A has inner measure zero and outer measure the same as C + C. Also, there is a subset A of the Cantor middle third set such that A+A is Bernstein in [0, 2]. On the other hand there is a perfect set C such that C + C is an interval I and there is no subset A ⊆ C with A + A Bernstein in I.
متن کاملSum-free Sets of Integers
A set S of integers is said to be sum-free if a, b e 5 implies a + b 6 S. In this paper, we investigate two new problems on sum-free sets: (1) Let f(k) denote the largest positive integer for which there exists a partition of (1, 2,... ,f(k)) into k sum-free sets, and let h(k) denote the largest positive integer for which there exists a partition of {1, 2, . . . , h(k)) into k sets which are su...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2011
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2011-02385-9