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arXiv · 1101.5851

New Bounds on cap sets

Michael Bateman·Nets Hawk Katz
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Abstract

We provide an improvement over Meshulam's bound on cap sets in $F_3^N$. We show that there exist universal $\epsilon>0$ and $C>0$ so that any cap set in $F_3^N$ has size at most $C {3^N \over N^{1+\epsilon}}$. We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.

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Michael Bateman, Nets Hawk Katz. 2011-01-31. New Bounds on cap sets. https://arxiv.org/abs/1101.5851

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