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New bounds on cap sets
Authors:
Michael Bateman and Nets Hawk Katz
Journal:
J. Amer. Math. Soc. 25 (2012), 585-613
MSC (2010):
Primary 11T71; Secondary 05D40
Posted:
November 29, 2011
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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.
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Additional Information
Michael Bateman
Affiliation:
Department of Mathematics, UCLA, Los Angeles, California 90095
Email:
bateman@math.ucla.edu
Nets Hawk Katz
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405-7000
Email:
nhkatz@indiana.edu
DOI:
http://dx.doi.org/10.1090/S0894-0347-2011-00725-X
PII:
S 0894-0347(2011)00725-X
Received by editor(s):
April 2, 2011
Received by editor(s) in revised form:
October 28, 2011
Posted:
November 29, 2011
Additional Notes:
The first author is supported by an NSF postdoctoral fellowship, DMS-0902490
The second author is partially supported by NSF grant DMS-1001607
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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