Abstract
Let X be a nonempty finite subset of \({\mathbb {R}}^d\) and \(X=\bigcup _{i=1}^m X_i\) a coloring with \(m<d\). In this paper we study the number of monochromatic lines generated by X. More specifically we give three results which establish that, under nontrivial assumptions, the number of monochromatic lines generated by X is \(\varTheta (|X|^2)\).
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Huicochea, M. On the Number of Monochromatic Lines in \(\pmb {\mathbb {R}}^d\). Discrete Comput Geom 65, 1061–1086 (2021). https://doi.org/10.1007/s00454-020-00210-2
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DOI: https://doi.org/10.1007/s00454-020-00210-2