Selectively balancing unit vectors

A. Blokhuis; H. Chen

doi:10.1007/s00493-016-3635-z

Selectively balancing unit vectors

Research output: Contribution to journal › Article › Academic › peer-review

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 ℝ n is asymptotically 1/2nlogn.

Original language	English
Pages (from-to)	67-74
Number of pages	8
Journal	Combinatorica
Volume	38
Issue number	1
DOIs	https://doi.org/10.1007/s00493-016-3635-z
Publication status	Published - 1 Feb 2018

Keywords

52A38
52C07

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10.1007/s00493-016-3635-z

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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 ℝ n is asymptotically 1/2nlogn.",

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AB - 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.

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