On Tomaszewski's Cube Vertices Problem

2022/12/03 by Yiming Li, Yuqin Zhang, Li, Yiming +2
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2212.01525

openalex publication_date 2022/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The following assertion was equivalent to a conjecture proposed by B. Tomaszewski : Let C be an n-dimensional unit cube and let H be a plank of thickness 1, both are centered at the origin, then no matter how to turn the cube around, C∩ H contains at least half of the cube's 2ⁿ vertices. A lower bound for the number of the vertices of C in C∩ H was obtained.

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