Sumsets in the Hypercube
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916208130916352 |
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| author | Alon, Noga Zamir, Or |
| author_facet | Alon, Noga Zamir, Or |
| contents | 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 $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16589 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sumsets in the Hypercube Alon, Noga Zamir, Or Combinatorics Discrete Mathematics 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 $1$. |
| title | Sumsets in the Hypercube |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2403.16589 |