An elementary additive doubling inequality
Combinatorics
2011-07-26 v2
Abstract
We prove an elementary additive combinatorics inequality, which says that if is a subset of an Abelian group, which has, in some strong sense, large doubling, then the difference set A-A has a large subset, which has small doubling.
Cite
@article{arxiv.1107.4494,
title = {An elementary additive doubling inequality},
author = {Misha Rudnev},
journal= {arXiv preprint arXiv:1107.4494},
year = {2011}
}
Comments
Withdrawn (permanently!) thanks to B. Bukh, and T. Tao who both pointed out that the trivial case of the zero difference makes the fourth moment a-priori quite large. Thus the condition, under which the "theorem" was claimed (referred to in the Abstract as "if $A$ is a subset of an Abelian group, which has, in some strong sense, large doubling") is never satisfied