A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?

DOI10.1017/S0963548309990265zbMath1193.52014OpenAlexW2166746278MaRDI QIDQ3552498

Endre Szabó, György Elekes, Miklós Simmonovits

Publication date: 22 April 2010

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0963548309990265

zbMATH Keywords

triple pointincidence graphochard problemparametrized family of curvessurface theoremSzmerédi-Trotter bound

Mathematics Subject Classification ID

Erd?s problems and related topics of discrete geometry (52C10) Other problems of combinatorial convexity (52A37) Configuration theorems in linear incidence geometry (51A20) Planar arrangements of lines and pseudolines (aspects of discrete geometry) (52C30)

Related Items (3)

Improved Elekes-Szabó type estimates using proximity ⋮ On triple intersections of three families of unit circles ⋮ Distinct Distances from Three Points

Cites Work

• Extremal problems in discrete geometry
• Repeated angles in the plane and related problems
• Circle grids and bipartite graphs of distances
• n points in the plane can determine \(n^{3/2}\) unit circles
• Arrangements of Lines with a Large Number of Triangles
• Crossing Numbers and Hard Erdős Problems in Discrete Geometry

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