A result of Fiz Pontiveros shows that if A is a random subset of ZN 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 ZN. In this paper we improve the bound to CN−2/3(logN)1/3, which is best possible up to the constant factor.Research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632.
Research supported by a Royal Society 2010 Anniversary Research Professorship