Finite point configurations in the plane, rigidity and Erdős problems

DOI10.1134/S0081543818080114zbMath1414.05101arXiv1805.08065MaRDI QIDQ2423216

Alexander Iosevich, J. Passant

Publication date: 21 June 2019

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.08065

zbMATH Keywords

\(G\)-frameworkErdős pinned-distance conjecture

Mathematics Subject Classification ID

Distance in graphs (05C12) Erd?s problems and related topics of discrete geometry (52C10)

Related Items (3)

On Erd\H{o}s Chains in the Plane ⋮ Note on the number of hinges defined by a point set in \(\mathbb{R}^2\) ⋮ Distribution of pinned distance trees in the plane \(\mathbb{F}_p^2\)

Cites Work

• On the Erdős distinct distances problem in the plane
• The number of different distances determined by n points in the plane
• Combinatorial complexity bounds for arrangements of curves and spheres
• Near optimal bounds for the Erdős distinct distances problem in high dimensions
• The number of different distances determined by a set of points in the Euclidean plane
• On distinct sums and distinct distances.
• The number of embeddings of minimally rigid graphs
• Rigid and Flexible Frameworks
• The Rigidity of Graphs
• Crossing Numbers and Hard Erdős Problems in Discrete Geometry
• Distinct Distances in Three and Higher Dimensions
• Rigidity, Graphs and Hausdorff Dimension
• On the Different Distances Determined by n Points
• On Sets of Distances of n Points
• Distinct distances in the plane
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