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 |
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Pages (from-to) | 67-74 |
Number of pages | 8 |
Journal | Combinatorica |
Volume | 38 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2018 |
Keywords
- 52A38
- 52C07