%0 Journal Article
%T On the Structure of Sets of Large Doubling
%A Allison Lewko
%A Mark Lewko
%J Mathematics
%D 2010
%I arXiv
%X 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 $\Lambda(4)$ set which does not contain large $B_2[g]$ or $B^\circ_2[g]$ sets.
%U http://arxiv.org/abs/1003.4561v4