The upper bound theorem for polytopes: an easy proof of its asymptotic version
نویسندگان
چکیده
منابع مشابه
The Upper Bound Theorem for Polytopes: an Easy Proof of Its Asymptotic Version
Since at least half of the d edges incident to a vertex u of a simple d-polytope P either all point “up” or all point “down,” v must be the unique “bottom” or “top” vertex of a face of P of dimension at least d/2. Thus the number of P’s vertices is at most twice the number of such high-dimensional faces, which is at most Ed,2 $ iG &Ynu) = O(nld/‘l), if P has n facets. This, in a nutshell, provi...
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We derive tight expressions for the maximum number of k-faces, 0 ≤ k ≤ d − 1, of the Minkowski sum, P1+⋯+Pr, of r convex d-polytopes P1, . . . , Pr in R, where d ≥ 2 and r < d, as a (recursively defined) function on the number of vertices of the polytopes. Our results coincide with those recently proved by Adiprasito and Sanyal [1]. In contrast to Adiprasito and Sanyal’s approach, which uses to...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 1995
ISSN: 0925-7721
DOI: 10.1016/0925-7721(95)00013-y