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Distance graphs and
sets of positive upper density in $\mathbb{R}^d$
Neil Lyall and Ákos Magyar |
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Vol. 13 (2020), No. 3, 685–700
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Abstract |
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We present a refinement and sharp extension of a result of Bourgain on finding configurations of points in general position in measurable subset of of positive upper density whenever to all proper -degenerate distance graphs. |
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Keywords
distance graphs, uniformity norms, geometric Ramsey theory
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Mathematical Subject Classification 2010
Primary: 11B30
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Milestones
Received: 23 March 2018
Revised: 11 January 2019
Accepted: 13 March 2019
Published: 15 April 2020
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Authors |
| Neil Lyall | |
| Department of Mathematics The University of Georgia Athens, GA United States |
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| Ákos Magyar | |
| Department of Mathematics The University of Georgia Athens, GA United States |
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