摘要
Let F = {A(i): 1 ≤ I ≤ t, t ≥ 2}, be a finite collection of finite, pairwise disjoint subsets of Z^+. Let S ⊂ R\{0} and A ⊂ Z^+ be finite sets. Denote by (The equation is abbreviated). For S and F as above we say that S is F-free if for every A(i), A(j) ∈ F, I ≠ j, S^(A(i)) ⋂ S^(A(j)) = ϕ. We prove that for S and F as above, S contains an F-free subset Q such that |Q| ≥ c(F)|S|, when c(F) is a positive constant depending only on F. This result generalizes earlier results of Erdos and Alon and Kleitman, on sum-free subsets. Several possible extensions are also discussed.
關鍵字
無資料延伸閱讀
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