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Sumsets in the Hypercube (2403.16589v2)

Published 25 Mar 2024 in math.CO and cs.DM

Abstract: A subset $S$ of the Boolean hypercube $\mathbb{F}_2n$ is a sumset if $S = A+A = {a + b \ | \ a, b\in A}$ for some $A \subseteq \mathbb{F}_2n$. We prove that the number of sumsets in $\mathbb{F}_2n$ is asymptotically $(2n-1)2{2{n-1}}$. Furthermore, we show that the family of sumsets in $\mathbb{F}_2n$ is almost identical to the family of all subsets of $\mathbb{F}_2n$ that contain a complete linear subspace of co-dimension $1$.

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