Green's sumset problem at density one half
Abstract
We investigate the size of subspaces in sumsets and show two main results. First, if A is a subset of F2n with density at least 1/2 - o(n-1/2) then A+A contains a subspace of co-dimension 1. Secondly, if A is a subset of F2n with density at least 1/2-o(1) then A+A contains a subspace of co-dimension o(n).
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