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Published March 2017 | Submitted
Journal Article Open

Freiman homomorphisms on sparse random sets


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.

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.

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