关于大倍集的结构
On the Structure of Sets of Large Doubling
摘要：
研究了有限集$A \subseteq \Z$的结构，其中$|A+A|$是大的.我们提出了一个组合的建设，作为一个反例，以自然的构造在追求一个“反Freiman”理论在添加剂组合。特别是，我们回答了O'Bryant提出的一个问题。我们的建设也回答了几个问题的性质有限工会的$B_2[g]$和$B^\circ_2[g]$集，并使我们能够构建一个$Λ(4)$集不包含大$B_2[g]$或$B^\circ_2[g]$集。
英文摘要：
We investigate the structure of finite sets $A \subseteq \Z$ where $|A+A|$ is large. We present a combinatorial construction that serves as a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. In particular, we answer a question along these lines posed by O'Bryant. Our construction also answers several questions about the nature of finite unions of $B_2[g]$ and $B^\circ_2[g]$ sets, and enables us to construct a $Λ(4)$ set which does not contain large $B_2[g]$ or $B^\circ_2[g]$ sets.
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