四色定理遇多面体形状
度量几何
2026-04-15 v1
摘要
我们考察四色问题中球面三角网顶点的解。我们将这些解按组合类型进行分类，表明每个普通类型 τ 由参数化为四维有理多面体凸锥 C_τ 中整数格点集合。存在一个整数二次型 Q_τ 作用于 C_τ，其对角线部分在格点上评估后等于相应三角网中三角形数的 3 倍。我们将这一结构与泰森的平坦锥结构模空间中八面体层鞘相关联。
引用
@article{arxiv.2604.12059,
title = {The Four Color Theorem meets Shapes of Polyhedra},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:2604.12059},
year = {2026}
}
备注
1. This paper is still a bit rough and preliminary. 2. This paper has a big companion java program. You don't need to use the program to understand the paper, but all the insights in the paper came from the program