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arXiv · 1605.05121

Selectively Balancing Unit Vectors

Aart Blokhuis·Hao Chen
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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 $\mathbb{R}^n$ is asymptotically $\frac{1}{2} n \log n$.

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Aart Blokhuis, Hao Chen. 2016-09-13. Selectively Balancing Unit Vectors. https://doi.org/10.1007/s00493-016-3635-z

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