Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka
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引用次数: 0
摘要
在本文中,我们定义并研究了一类多边形,我们称之为 "顶点生成的 "多边形,由 0 元和 n 元维面的平均值组成。我们展示了关于这一类多面体的许多结果,其中包括:这一类多面体包含所有多面体;这一类多面体在维数$n=2$时是密集的;任何多面体都可以与一个多面体相加,从而使其和在这一类多面体中;著名的 "莫里定理 "的一种强形式在这一类多面体中成立。我们为每个多面体引入了一个参数,用来度量它离顶点生成有多远,并证明当这个参数很小时,强覆盖性质成立。
In this paper we define and investigate a class of polytopes which we call
"vertex generated" consisting of polytopes which are the average of their $0$
and $n$ dimensional faces. We show many results regarding this class, among
them: that the class contains all zonotopes, that it is dense in dimension
$n=2$, that any polytope can be summed with a zonotope so that the sum is in
this class, and that a strong form of the celebrated "Maurey Lemma" holds for
polytopes in this class. We introduce for every polytope a parameter which
measures how far it is from being vertex-generated, and show that when this
parameter is small, strong covering properties hold.