On the number of monochromatic lines in \(\mathbb{R}^d\)

DOI10.1007/s00454-020-00210-2zbMath1462.52042OpenAlexW3031346076MaRDI QIDQ2022615

Mario Huicochea

Publication date: 29 April 2021

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-020-00210-2

zbMATH Keywords

coloringSzemerédi-Trotter theoremgenerated hyperplanesmonochromatic lines

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Other problems of combinatorial convexity (52A37) Combinatorial complexity of geometric structures (52C45)

Cites Work

• Unnamed Item
• On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
• The Sylvester-Gallai theorem, colourings and algebra
• On monochrome lines and hyperplanes
• Essential dimension and the flats spanned by a point set
• Extending Erdős-Beck's theorem to higher dimensions
• A quantitative variant of the multi-colored Motzkin-Rabin theorem
• A survey of Sylvester's problem and its generalizations

This page was built for publication: On the number of monochromatic lines in \(\mathbb{R}^d\)