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A system of ℓ linear equations in p unknowns Mx = b is said to have the removal property if every set S ⊆ {1,...,n} which contains o(np − ℓ) solutions of Mx = b can be turned into a set S′ containing no solution of Mx = b, by the removal of o(n) elements. Green [GAFA 2005] proved that a single homogenous linear equation always has the removal property, and conjectured that...
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