Non-averaging Subsets and Non-vanishing Transversals
Non-averaging Subsets and Non-vanishing Transversals
复制标题
非平均子集和非零横截面
DOI：
10.1006/jcta.1998.2926
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
I. Ruzsa
中科院分区：
文献类型：
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作者：
N. Alon;I. Ruzsa
结果表明，每组九个数包含一个大小为？(n1/6)的子集，其中没有一个元素是两个或多个其他元素的平均值。这改善了雅培的结果。还证明了对每一个？>0和每一个m&>m(？)以下内容成立。如果集合{A1，？，Am的每个基数子集至少m1+？，则存在1？a1，？，Am，使得集合{a1，？，Am}的每个非空子集的和不为零。这几乎是紧绷的。这两个定理的证明是相似的，并结合了简单的概率方法与组合和数论工具。
It is shown that every set ofnintegers contains a subset of size?(n1/6) in which no element is the average of two or more others. This improves a result of Abbott. It is also proved that for every?>0 and everym>m(?) the following holds. IfA1,?,Amaremsubsets of cardinality at leastm1+?each, then there area1?A1,?,am?Amso that the sum of every nonempty subset of the set {a1,?,am} is nonzero. This is nearly tight. The proofs of both theorems are similar and combine simple probabilistic methods with combinatorial and number theoretic tools.