论文标题
添加剂维度和集合的增长
Additive dimension and the growth of sets
论文作者
论文摘要
我们开发了添加尺寸$ {\ rm dim}（a）$的理论，即集合$ a $的最大解离子集的大小。结果表明，添加剂维度与我们集合$ a $ a $ a $ a $ na $的增长密切相关。我们采用这种方法来证明，对于任何小型乘法亚组$γ$序列$ |nγ| $的生长非常快。同样，我们为总和 - 生产现象和Balog-wooley分解 - 型型结果获得了一系列应用。
We develop the theory of the additive dimension ${\rm dim} (A)$, i.e. the size of a maximal dissociated subset of a set $A$. It was shown that the additive dimension is closely connected with the growth of higher sumsets $nA$ of our set $A$. We apply this approach to demonstrate that for any small multiplicative subgroup $Γ$ the sequence $|nΓ|$ grows very fast. Also, we obtain a series of applications to the sum--product phenomenon and to the Balog--Wooley decomposition--type results.
