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Difference sets in higher dimensions
| Content Provider | Scilit |
|---|---|
| Author | Mudgal, Akshat |
| Copyright Year | 2020 |
| Description | Let d ≥ 3 be a natural number. We show that for all finite, non-empty sets $A \subseteq \mathbb{R}^d$ that are not contained in a translate of a hyperplane, we have $\begin{equation*} |A-A| \geq (2d-2)|A| - O_d(|A|^{1- \delta}),\end{equation*}$ where δ > 0 is an absolute constant only depending on d. This improves upon an earlier result of Freiman, Heppes and Uhrin, and makes progress towards a conjecture of Stanchescu. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3A3E698C5C926A349054DE2F905DA12E/S0305004120000298a.pdf/div-class-title-difference-sets-in-higher-dimensions-div.pdf |
| Ending Page | 480 |
| Page Count | 14 |
| Starting Page | 467 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004120000298 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 171 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2021-11-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
