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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. doi:10.1093/qmath/haw058.

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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
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URLURL TypeDescription Paper
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.
Funding AgencyGrant Number
European Research Council (ERC)676632
Issue or Number:1
Record Number:CaltechAUTHORS:20190812-163000651
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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,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97841
Deposited By: Melissa Ray
Deposited On:16 Aug 2019 20:25
Last Modified:16 Nov 2021 17:34

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