An Example Concerning Set Addition in $\mathbb{F}_2^n$

Proceedings of the Steklov Institute of Mathematics, pp. 105-108, 2019.

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Abstract:

We construct sets A and B in a vector space over \(\mathbb{F}\) with the property that A is “statistically” almost closed under addition by B in the sense that a + b almost always lies in A when a ∈ A and b ∈ B, but which is extremely far from being “combinatorially” almost closed under addition by B: if A′⊂ A, B′⊂ B and A′ + B′ is compar...More

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