The structure of d-dimensional sets with small sumset
نویسندگان
چکیده
منابع مشابه
Properties of two-dimensional sets with small sumset
Let A, B ⊆ R be finite, nonempty subsets, let s ≥ 2 be an integer, and let h1(A,B) denote the minimal number t such that there exist 2t (not necessarily distinct) parallel lines, l1, . . . , lt, l ′ 1, . . . , l ′ t , with A ⊆ ⋃t i=1 li and B ⊆ ⋃t i=1 l ′ i . Suppose h1(A,B) ≥ s. Then we show that: (a) if ||A| − |B|| ≤ s and |A|+ |B| ≥ 4s − 6s+ 3, then |A+B| ≥ (2− 1 s )(|A| + |B|)− 2s+ 1; (b) i...
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Given a set A ⊆ Z/NZ we may form a Cayley sum graph GA on vertex set Z/NZ by joining i to j if and only if i + j ∈ A. We investigate the extent to which performing this construction with a random set A simulates the generation of a random graph, proving that the clique number of GA is a.s. O(logN). This shows that Cayley sum graphs can furnish good examples of Ramsey graphs. To prove this resul...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2010
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.08.004