Erdős’s unit distance problem

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

We survey some problems and results around one of Paul Erdős’s favorite questions, first published 70 years ago: What is the maximum number of times that the unit distance can occur among n points in the plane? This simple and beautiful question has generated a lot of important research in discrete geometry, in extremal combinatorics, in additive number theory, in Fourier analysis, in algebra, and in other fields, but we still do not seem to be close to a satisfactory answer.

Original languageEnglish
Title of host publicationOpen Problems in Mathematics
PublisherSpringer International Publishing
Pages459-477
Number of pages19
ISBN (Electronic)9783319321622
ISBN (Print)9783319321608
DOIs
Publication statusPublished - Jan 1 2016

Fingerprint

Extremal Combinatorics
Additive number Theory
Discrete Geometry
Fourier Analysis
Algebra
Unit
Combinatorics
Geometry

Keywords

  • Combinatorial geometry
  • Diameter graph
  • Geometric graph
  • Unit circle
  • Unit distance

ASJC Scopus subject areas

  • Mathematics(all)
  • Economics, Econometrics and Finance(all)
  • Business, Management and Accounting(all)

Cite this

Szemerédi, E. (2016). Erdős’s unit distance problem. In Open Problems in Mathematics (pp. 459-477). Springer International Publishing. https://doi.org/10.1007/978-3-319-32162-2_15

Erdős’s unit distance problem. / Szemerédi, E.

Open Problems in Mathematics. Springer International Publishing, 2016. p. 459-477.

Research output: Chapter in Book/Report/Conference proceedingChapter

Szemerédi, E 2016, Erdős’s unit distance problem. in Open Problems in Mathematics. Springer International Publishing, pp. 459-477. https://doi.org/10.1007/978-3-319-32162-2_15
Szemerédi E. Erdős’s unit distance problem. In Open Problems in Mathematics. Springer International Publishing. 2016. p. 459-477 https://doi.org/10.1007/978-3-319-32162-2_15
Szemerédi, E. / Erdős’s unit distance problem. Open Problems in Mathematics. Springer International Publishing, 2016. pp. 459-477
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