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.
Submitted - 1603.01734.pdf