Sets of points determining only acute angles and some related colouring problems

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Abstract

We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
Original languageEnglish
Article numberR12
Number of pages24
JournalThe Electronic Journal of Combinatorics
Volume13
Issue number1
Publication statusPublished - 15 Feb 2006

Keywords

  • point sets
  • probabilistic method
  • acute angles

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