Sum-free sets, coloured graphs and designs
نویسندگان
چکیده
منابع مشابه
Sum-Free Sets and Related Sets
A set A of integers is sum-free if A\(A+A) = ;. Cameron conjectured that the number of sum-free sets A f1; : : : ; Ng is O(2 N=2). As a step towards this conjecture, we prove that the number of sets A f1
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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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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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We show that the number of subsets of {1, 2, ..., n} with no solution to x1+x2+ ...+xk = y1+y2+ ..+yl for k ≥ 4l−1 is at most c2 where θ = k−l k .
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1976
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700013343