Variations on the theme of repeated distances

P. Erdős, J. Pach

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined by n points in ℝd, d≥4. We also give asymptotically tight upper bounds on the total number of occurrences of the "favourite" distances from n points in ℝd, d≥4. Related results are proved for distances determined by n disjoint compact convex sets in ℝ2.

Original languageEnglish
Pages (from-to)261-269
Number of pages9
JournalCombinatorica
Volume10
Issue number3
DOIs
Publication statusPublished - Sep 1990

Fingerprint

Compact Convex Set
Error term
Disjoint
Upper bound
Unit
Estimate

Keywords

  • AMS subject classification (1980): 52A37, 52A40

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

Variations on the theme of repeated distances. / Erdős, P.; Pach, J.

In: Combinatorica, Vol. 10, No. 3, 09.1990, p. 261-269.

Research output: Contribution to journalArticle

Erdős, P. ; Pach, J. / Variations on the theme of repeated distances. In: Combinatorica. 1990 ; Vol. 10, No. 3. pp. 261-269.
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