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arXiv · 1803.08916

Distance Graphs and sets of positive upper density in $\mathbb{R}^d$

Neil Lyall·Akos Magyar
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Abstract

We present a sharp extension of a result of Bourgain on finding configurations of $k+1$ points in general position in measurable subset of $\mathbb{R}^d$ of positive upper density whenever $d\geq k+1$ to all proper $k$-degenerate distance graphs.

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BibTeXRIS

Neil Lyall, Akos Magyar. 2018-03-23. Distance Graphs and sets of positive upper density in $\mathbb{R}^d$. https://doi.org/10.2140/apde.2020.13.685

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