Current browse context:
math
Change to browse by:
References & Citations
Mathematics > Combinatorics
Title: Sumsets in the Hypercube
(Submitted on 25 Mar 2024 (v1), last revised 16 Apr 2024 (this version, v2))
Abstract: A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = A+A = \{a + b \ | \ a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. We prove that the number of sumsets in $\mathbb{F}_2^n$ is asymptotically $(2^n-1)2^{2^{n-1}}$. Furthermore, we show that the family of sumsets in $\mathbb{F}_2^n$ is almost identical to the family of all subsets of $\mathbb{F}_2^n$ that contain a complete linear subspace of co-dimension $1$.
Submission history
From: Or Zamir [view email][v1] Mon, 25 Mar 2024 09:59:44 GMT (19kb)
[v2] Tue, 16 Apr 2024 13:36:56 GMT (19kb)
Link back to: arXiv, form interface, contact.