Lyall, Neil and Magyar, Ákos (2020) Distance graphs and sets of positive upper density in Rd. ANALYSIS & PDE, 13 (3). pp. 685-700. ISSN 2157-5045
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Official URL: http://doi.org/10.2140/apde.2020.13.685
Abstract
We present a refinement and sharp extension of a result of Bourgain on finding configurations of kC1 points in general position in measurable subset of Rd of positive upper density whenever d ≥ k C1 to all proper k-degenerate distance graphs. ©2020 Mathematical Sciences Publishers.
| Item Type: | Article |
|---|---|
| Additional Information: | Cited By :5 Export Date: 23 May 2022 Funding details: National Science Foundation, NSF, 1702411 Funding details: Simons Foundation, SF, 1600840, 245792, ERC-AdG 321104 Funding text 1: Lyall was partially supported by grant NSF-DMS 1702411 and the Simons Foundation Collaboration Grant for Mathematicians 245792. Magyar was partially supported by grant NSF-DMS 1600840 and ERC-AdG 321104. MSC2010: 11B30. Keywords: distance graphs, uniformity norms, geometric Ramsey theory. |
| Uncontrolled Keywords: | Distance graphs, Geometric Ramsey theory, Uniformity norms |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA166-QA166.245 Graphs theory / gráfelmélet |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 23 May 2022 12:03 |
| Last Modified: | 23 May 2022 12:03 |
| URI: | http://real.mtak.hu/id/eprint/142995 |
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