Selectively balancing unit vectors

A. Blokhuis, H. Chen

Research output: Contribution to journalArticleAcademicpeer-review


A set U of unit vectors is selectively balancing if one can find two disjoint subsets U+ and U-, not both empty, such that the Euclidean distance between the sum of U+ and the sum of U- is smaller than 1. We prove that the minimum number of unit vectors that guarantee a selectively balancing set in ℝ n is asymptotically 1/2nlogn.
Original languageEnglish
Pages (from-to)67-74
Number of pages8
Issue number1
Publication statusPublished - 1 Feb 2018


  • 52A38
  • 52C07

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