English

On Tomaszewski's Cube Vertices Problem

Combinatorics 2023-02-28 v2

Abstract

The following assertion was equivalent to a conjecture proposed by B. Tomaszewski : Let CC be an nn-dimensional unit cube and let HH be a plank of thickness 11, both are centered at the origin, then no matter how to turn the cube around, CHC\cap H contains at least half of the cube's 2n2^n vertices. A lower bound for the number of the vertices of CC in CHC\cap H was obtained.

Keywords

Cite

@article{arxiv.2212.01525,
  title  = {On Tomaszewski's Cube Vertices Problem},
  author = {Yiming Li and Yuqin Zhang and Miao Fu},
  journal= {arXiv preprint arXiv:2212.01525},
  year   = {2023}
}
R2 v1 2026-06-28T07:21:03.075Z