Selectively Balancing Unit Vectors

Abstract

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 ℝn is asymptotically 1/2nlogn.

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Correspondence to Hao Chen.

Additional information

H. Chen is supported by the Deutsche Forschungsgemeinschaft within the Research Training Group ‘Methods for Discrete Structures’ (GRK 1408) and by NWO/DIAMANT grant number 613.009.031.

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Blokhuis, A., Chen, H. Selectively Balancing Unit Vectors. Combinatorica 38, 67–74 (2018). https://doi.org/10.1007/s00493-016-3635-z

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Mathematics Subject Classification (2000)

  • 52C07
  • 52A38