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arXiv · 1703.01036

An example concerning set addition in F_2^n

Ben Green·Daniel Kane
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Abstract

We construct sets $A, B$ in a vector space over $\mathbb{F}_2$ 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 $a \in A, b \in B$, but which is extremely far from being "combinatorially" almost closed under addition by $B$: if $A' \subset A$, $B' \subset B$ and $A' + B'$ is comparable in size to $A'$ then $|B'| \lessapprox |B|^{1/2}$.

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Ben Green, Daniel Kane. 2017-11-13. An example concerning set addition in F_2^n. https://arxiv.org/abs/1703.01036

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