七点平面上的 Sierksma 猜想的初等证明
计算机视觉与模式识别
2026-04-21 v1 多媒体
机器人学
摘要
我们给出一种新的简单几何证明，证明平面上的任意七个点可分割为三个集合的四个 Tverberg 分区。这一证明是 Sierksma 猜想中唯一被确认的非平凡情形。此前的证明（如 Stephan Hell 所著）依赖于拓扑论证明。
引用
@article{arxiv.2604.18484,
title = {XEmbodied: A Foundation Model with Enhanced Geometric and Physical Cues for Large-Scale Embodied Environments},
author = {Kangan Qian and ChuChu Xie and Yang Zhong and Jingrui Pang and Siwen Jiao and Sicong Jiang and Zilin Huang and Yunlong Wang and Kun Jiang and Mengmeng Yang and Hao Ye and Guanghao Zhang and Hangjun Ye and Guang Chen and Long Chen and Diange Yang},
journal= {arXiv preprint arXiv:2604.18484},
year = {2026}
}
备注
15 pages, 5 figures