On exponential Freiman dimension
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908714711121920 |
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| author | Lim, Jeck Mudgal, Akshat Pohoata, Cosmin Shao, Xuancheng |
| author_facet | Lim, Jeck Mudgal, Akshat Pohoata, Cosmin Shao, Xuancheng |
| contents | The exponential Freiman dimension of a finite set $A \subset \mathbb{R}^{m}$, introduced by Green and Tao in 2006, represents the largest positive integer $d$ for which $A$ contains the vertices of a non-degenerate $d$-dimensional parallelepiped. For every $d \geq 1$, we precisely determine the largest constant $C_{d}>0$ (exponential in $d$) for which $$|A+A| \geq C_{d}|A| - O_{d}(1)$$ holds for all sets $A$ with exponential Freiman dimension $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On exponential Freiman dimension Lim, Jeck Mudgal, Akshat Pohoata, Cosmin Shao, Xuancheng Combinatorics Number Theory The exponential Freiman dimension of a finite set $A \subset \mathbb{R}^{m}$, introduced by Green and Tao in 2006, represents the largest positive integer $d$ for which $A$ contains the vertices of a non-degenerate $d$-dimensional parallelepiped. For every $d \geq 1$, we precisely determine the largest constant $C_{d}>0$ (exponential in $d$) for which $$|A+A| \geq C_{d}|A| - O_{d}(1)$$ holds for all sets $A$ with exponential Freiman dimension $d$. |
| title | On exponential Freiman dimension |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2512.14403 |