Economical coverings of sets of lattice points

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Let t(n, d) be the minimum number t such that there are t of the nd lattice points {Mathematical expression} so that the (2t) lines that they determine cover all the above nd lattice points. We prove that for every integer d≥2 there are two positive constants c1=c1(d) and c2=c2(d) such that for every n {Mathematical expression} The special case d=2 settles a problem of Erdös and Purdy.

Original languageEnglish (US)
Pages (from-to)225-230
Number of pages6
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Sep 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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