Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 62: Issue 1
A Note on a Problem of Erdős About Rich Distances
Author:
Krishnendu Bhowmick Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria

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Pages:
89–94
Online Publication Date:
27 Mar 2025
Publication Date:
09 Apr 2025
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2025.04332
Keywords:
Erdős problems; distance probelms
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A question of Erdős asked whether there exists a set of 𝑛 points such that 𝑐 ⋅ 𝑛 distances occur more than 𝑛 times. We provide an affirmative answer to this question, showing that there exists a set of 𝑛 points such that n4 distances occur more than 𝑛 times. We also present a generalized version, finding a set of 𝑛 points where 𝑐𝑚 ⋅ 𝑛 distances occurring more than 𝑛 + 𝑚 times.

  • [1]

    P. Brass, W. Moser, and J. Pach. Research problems in discrete geometry. Springer, New York, 2005.

  • [2]

    P. Erdős. Some old and new problems in various branches of combinatorics. volume 165/166, pages 227–231. 1997. Graphs and combinatorics (Marseille, 1995).

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  • [3]

    P. Erdős and J. Pach. Variations on the theme of repeated distances. Combinatorica, 10(3):261–269, 1990.

  • [4]

    A. Sheffer. Distinct distances: Open problems and current bounds. [v1] 2014, [v3] 2018.

  • [5]

    J. Spencer, E. Szemerédi, and W. Trotter, Jr. Unit distances in the Euclidean plane. In Graph theory and combinatorics (Cambridge, 1983), pages 293–303. Academic Press, London, 1984.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

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Gábor SÁGI (Rényi Institute of Mathematics)

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  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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