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Freiman homomorphisms on sparse random sets

Conlon, D. and Gowers, W. T. (2017) Freiman homomorphisms on sparse random sets. Quarterly Journal of Mathematics, 68 (1). pp. 275-300. ISSN 0033-5606. https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000651

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Abstract

A result of Fiz Pontiveros shows that if A is a random subset of ℤ_N where each element is chosen independently with probability N^(−1/2+o(1))⁠, then with high probability every Freiman homomorphism defined on A can be extended to a Freiman homomorphism on the whole of ℤ_N⁠. In this paper, we improve the bound to CN^(−2/3)(logN)^(1/3)⁠, which is best possible up to the constant factor.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1093/qmath/haw058DOIArticle
https://academic.oup.com/qjmath/article-abstract/68/1/275/2967153PublisherArticle
https://arxiv.org/abs/1603.01734arXivDiscussion Paper
ORCID:
AuthorORCID
Conlon, D.0000-0001-5899-1829
Additional Information:© 2017 Oxford University Press. Conlon research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. Gowers research supported by a Royal Society 2010 Anniversary Research Professorship.
Funders:
Funding AgencyGrant Number
Royal SocietyUNSPECIFIED
European Research Council (ERC)676632
Issue or Number:1
Record Number:CaltechAUTHORS:20190812-163000651
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000651
Official Citation:D. Conlon, W. T. Gowers, Freiman homomorphisms on sparse random sets, The Quarterly Journal of Mathematics, Volume 68, Issue 1, March 2017, Pages 275–300, https://doi.org/10.1093/qmath/haw058
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97841
Collection:CaltechAUTHORS
Deposited By: Melissa Ray
Deposited On:16 Aug 2019 20:25
Last Modified:03 Oct 2019 21:35

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