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On the number of rich lines in high dimensional real vector spaces

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Publication:309656
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DOI10.1007/s00454-016-9774-6zbMath1351.52016arXiv1412.7025OpenAlexW1549113609MaRDI QIDQ309656

Zachary Scherr, Márton Hablicsek

Publication date: 7 September 2016

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

Full work available at URL: https://arxiv.org/abs/1412.7025


zbMATH Keywords

combinatorial geometryincidence geometrypolynomial partitioning


Mathematics Subject Classification ID

Partitions of sets (05A18) Erd?s problems and related topics of discrete geometry (52C10)


Related Items

Incidences with Curves in ℝ d ⋮ Concentration estimates for algebraic intersections ⋮ Incidences between points and lines in \({\mathbb {R}}^4\) ⋮ Incidences with curves in \(\mathbb{R}^d\)



Cites Work

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  • The Szemerédi-Trotter theorem in the complex plane
  • On the Erdős distinct distances problem in the plane
  • Simple proofs of classical theorems in discrete geometry via the Guth-Katz polynomial partitioning technique
  • A Szemerédi-Trotter type theorem in \(\mathbb R^4\)
  • Extremal problems in discrete geometry
  • Incidence bounds on multijoints and generic joints
  • A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS
  • On the Number of Incidences Between Points and Curves
  • On the number of rich lines in truly high dimensional sets
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