Multiplicities of interpoint distances in finite planar sets

P. Erdős, Peter C. Fishburn

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.

Original languageEnglish
Pages (from-to)141-147
Number of pages7
JournalDiscrete Applied Mathematics
Volume60
Issue number1-3
DOIs
Publication statusPublished - Jun 23 1995

Fingerprint

Multiplicity
n-gon
Partial
Unit
Subset
Review

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Multiplicities of interpoint distances in finite planar sets. / Erdős, P.; Fishburn, Peter C.

In: Discrete Applied Mathematics, Vol. 60, No. 1-3, 23.06.1995, p. 141-147.

Research output: Contribution to journalArticle

Erdős, P. ; Fishburn, Peter C. / Multiplicities of interpoint distances in finite planar sets. In: Discrete Applied Mathematics. 1995 ; Vol. 60, No. 1-3. pp. 141-147.
@article{d57af2f87f034bf9a5826c214ef3beef,
title = "Multiplicities of interpoint distances in finite planar sets",
abstract = "What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.",
author = "P. Erdős and Fishburn, {Peter C.}",
year = "1995",
month = "6",
day = "23",
doi = "10.1016/0166-218X(94)00046-G",
language = "English",
volume = "60",
pages = "141--147",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Multiplicities of interpoint distances in finite planar sets

AU - Erdős, P.

AU - Fishburn, Peter C.

PY - 1995/6/23

Y1 - 1995/6/23

N2 - What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.

AB - What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.

UR - http://www.scopus.com/inward/record.url?scp=0000593682&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000593682&partnerID=8YFLogxK

U2 - 10.1016/0166-218X(94)00046-G

DO - 10.1016/0166-218X(94)00046-G

M3 - Article

VL - 60

SP - 141

EP - 147

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -