Vertex generated polytopes
| Autor: | Artstein-Avidan, Shiri, Falah, Tomer, Slomka, Boaz A. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: replacement of 2306.15293, paper no. 2/3. 22 pages, 2 figures |
| Databáze: | arXiv |
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