New bounds on cap sets

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https://doi.org/10.1090/S0894-0347-2011-00725-X

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2012

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American Mathematical Society

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https://hdl.handle.net/2022/19057

Abstract

We provide an improvement over Meshulam's bound on cap sets in F3N. We show that there exist universal ϵ>0 and $ C > 0$ so that any cap set in F3N has size at most C3NN1+e. We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.

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Bateman, M., & Katz, N. H. (2012). New bounds on cap sets. Journal of the American Mathematical Society, 25(2), 585-613. http://dx.doi.org/10.1090/S0894-0347-2011-00725-X

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© 2011 American Mathematical Society. Reverts to public domain 28 years from publication.

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Faculty Publications and Research