A combinatorial distinction between unit circles and straight lines: How many coincidences can they have?

György Elekes, Miklós Simonovits, Endre Szabó

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We give a very general sufficient condition for a one-parameter family of curves not to have n members with too many (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)

Original languageEnglish
Pages (from-to)691-705
Number of pages15
JournalCombinatorics Probability and Computing
Volume18
Issue number5
DOIs
Publication statusPublished - Sep 1 2009

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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