Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910823078690816 |
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| author | Bedert, Benjamin |
| author_facet | Bedert, Benjamin |
| contents | A set $B$ is said to be \emph{sum-free} if there are no $x,y,z\in B$ with $x+y=z$. We show that there exists a constant $c>0$ such that any set $A$ of $n$ integers contains a sum-free subset $A'$ of size $|A'|\geqslant n/3+c\log \log n$. This answers a longstanding problem in additive combinatorics, originally due to Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series Bedert, Benjamin Number Theory Classical Analysis and ODEs Combinatorics A set $B$ is said to be \emph{sum-free} if there are no $x,y,z\in B$ with $x+y=z$. We show that there exists a constant $c>0$ such that any set $A$ of $n$ integers contains a sum-free subset $A'$ of size $|A'|\geqslant n/3+c\log \log n$. This answers a longstanding problem in additive combinatorics, originally due to Erdős. |
| title | Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series |
| topic | Number Theory Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2502.08624 |