New Bounds on cap sets
Classical Analysis and ODEs
2011-04-05 v2 Combinatorics
Number Theory
Abstract
We provide an improvement over Meshulam's bound on cap sets in . We show that there exist universal and so that any cap set in has size at most . We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.
Keywords
Cite
@article{arxiv.1101.5851,
title = {New Bounds on cap sets},
author = {Michael Bateman and Nets Hawk Katz},
journal= {arXiv preprint arXiv:1101.5851},
year = {2011}
}
Comments
New version: The most substantive change is the correction of our overstatement of the efficacy of the asymmetric Balog-Szemeredi-Gowers lemma. (Thanks to Izabella Laba and Olof Sisask for pointing this out.) 38 pages