关于离解基的大小
On the size of dissociated bases
摘要：
证明了阿贝尔群的有限子集的极大解离子集的大小至多相差一个对数因子。另一方面，我们证明了集合$\{0,1\}^n\seq\Z^n$具有大小为$\Ome(n\log n)$的解离子集;由于$\Z^n$的标准基是大小为$n$的$\{0,1\}^n$的最大解离子集，所以刚才提到的结果本质上是尖锐的。
英文摘要：
We prove that the sizes of the maximal dissociated subsets of a given finite subset of an abelian group differ by a logarithmic factor at most. On the other hand, we show that the set $\{0,1\}^n\seq\Z^n$ possesses a dissociated subset of size $\Ome(n\log n)$; since the standard basis of $\Z^n$ is a maximal dissociated subset of $\{0,1\}^n$ of size $n$, the result just mentioned is essentially sharp.
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