任意有限群都是某个二元凸多面体的群
组合数学
2017-09-18 v2
摘要
对于任意给定的有限群，Schulte和Williams (2015) 证明了存在一个凸多面体，其组合自同构构成一个同构于该给定群的群。本文给出了一个更强结果的更简短证明：我们为给定有限群构造的凸多面体是二元的，甚至在Naddef和Pulleyblank (1981)意义下是组合的；其骨架的直径至多为2；该多面体的任意组合自同构均由空间的某个等距同构诱导；骨架的任意自同构都是组合自同构。
引用
@article{arxiv.1602.02987,
title = {Any Finite Group is the Group of Some Binary, Convex Polytope},
author = {Jean-Paul Doignon},
journal= {arXiv preprint arXiv:1602.02987},
year = {2017}
}
备注
The revised version gives a better proof for the property of the automorphisms of the polytope skeleton (Theorem 1, (v)). It also takes into account suggestions made by two anonymous referees. The final paper is to appear in Discrete and Computational Geometry