对称多胞形的极值性质及其应用  

Extremal Properties of Symmetric Polytopes and Applications

作　　者：何斌吾[1] 杨柳[1] 

机构地区：[1]上海大学数学系,上海200444

出　　处：《数学年刊（A辑）》2006年第5期615-624,共10页Chinese Annals of Mathematics

基　　金：上海市教育委员会科研基金(No.214667)资助的项目.

摘　　要：凸多胞形现代理论的主要成就是被称之为Dehn-Sommerville关系的上界定理和下界定理,它们属于凸多胞形的经典组合理论．本文建立了关于对称凸多胞形的两个极值定理,它们可视为凸多胞形度量理论中的上界定理和下界定理,另外给出了两个极值定理的一个应用．The main achievements in the modern theory of convex polytopes are the Upper Bound Theorem and the Lower Bound Theorem called as the Dehn-Sommerville Relations, these belong to the classical combinatorial theory of convex polytopes. In this paper, two extremal theorems little known for symmetric polytopes are established, they may be seen as the Upper Bound Theorem and the Lower Bound Theorem of the metric theory of convex polytopes. In addition, some applications are given.

关 键 词：凸多胞形 对称多胞形 简单多胞形 上界定理 下界定理 

分 类 号：O174.13[理学—数学]