PreprintCC BY 4.0arXiv
Unbalancing unit vectors
Abstract
We show that for every n unit vectors v1, …, vn in the d-dimensional Euclidean space, there exist signs ε1, …, εn ∈ {± 1} such that lVert ε1 v1 + … + εn vn rVert ≥ √(2n − d), and we characterize the equality cases.
Related
BibTeX
@misc{jiang2026unbalancing,
title = {{Unbalancing unit vectors}},
author = {Zilin Jiang and Jeck Lim and Skand Parvatikar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31389},
eprint = {2609.31389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31389},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unbalancing unit vectors
AU - Zilin Jiang
AU - Jeck Lim
AU - Skand Parvatikar
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31389
UR - https://arxiv.org/abs/2609.31389
AB - We show that for every n unit vectors v_1, …, v_n in the d-dimensional Euclidean space, there exist signs ε_1, …, ε_n ∈ {± 1} such that lVert ε_1 v_1 + … + ε_n v_n rVert ≥ √(2n − d), and we characterize the equality cases.
ER -