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PreprintarXiv licencearXiv

An optimal constant for vector balancing with permutations

  • Jonathan Niles-Weed
  • Shay Sadovsky
  • Jacob Shkrob
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Abstract

We present a version of the vector balancing problem in which each vector may be given a sign and a permutation of its coordinates. We prove that this vector balancing problem and its corresponding prefix problem admit an explicit bound, and we further show that it is asymptotically optimal in the dimension. Our method of proof is purely geometric.

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Cite

BibTeXRIS
BibTeX
@misc{nilesweed2026optimal,
  title = {{An optimal constant for vector balancing with permutations}},
  author = {Jonathan Niles-Weed and Shay Sadovsky and Jacob Shkrob},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02127},
  eprint = {2610.02127},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02127},
}
RIS
TY  - UNPB
TI  - An optimal constant for vector balancing with permutations
AU  - Jonathan Niles-Weed
AU  - Shay Sadovsky
AU  - Jacob Shkrob
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02127
UR  - https://arxiv.org/abs/2610.02127
AB  - We present a version of the vector balancing problem in which each vector may be given a sign and a permutation of its coordinates. We prove that this vector balancing problem and its corresponding prefix problem admit an explicit bound, and we further show that it is asymptotically optimal in the dimension. Our method of proof is purely geometric.
ER  -