On the Structure of Sets of Large Doubling

Details On the Structure of Sets of Large Doubling On the Structure of Sets of Large Doubling

2010-03-24

arxiv.org/abs/1003.4561v4

Mathematics

Classical Analysis and ODEs

23 pages, changed title, revised version reflects work of Meyer that we were previously unaware of

Scientific paper

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.

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