منابع مشابه
Generalized Sum - Free Subsets 751
Let F {A(1): < i < t, t 2}, be a finite collection of finite, palrwlse disjoint subsets of Z+. Let SC R\{0} and A Z+ be finite sets. Denote by S A {i=isi:a A, i S, the s i are not ncesarily dlstinct }. For S and F as above we say that S is F-free if for every A(i), A(J) F, i J, SA(1)(% SA(j) . We prove that for S and F as above, S contains an F-free subset Q such that This result generalizes ea...
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We characterize the structure of maximum-size sum-free subsets of a random subset of an Abelian group G. In particular, we determine the threshold above which, with high probability as |G| → ∞, each such subset is contained in some maximum-size sum-free subset of G, whenever q divides |G| for some (fixed) prime q with q ≡ 2 (mod 3). Moreover, in the special case G = Z2n, we determine the sharp ...
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Cameron and Erdős [6] raised the question of how many maximal sum-free sets there are in {1, . . . , n}, giving a lower bound of 2bn/4c. In this paper we prove that there are in fact at most 2(1/4+o(1))n maximal sum-free sets in {1, . . . , n}. Our proof makes use of container and removal lemmas of Green [8, 9] as well as a result of Deshouillers, Freiman, Sós and Temkin [7] on the structure of...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1990
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s016117129000103x