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 be an -dimensional unit cube and let be a plank of thickness , both are centered at the origin, then no matter how to turn the cube around, contains at least half of the cube's vertices. A lower bound for the number of the vertices of in 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}
}