A Geometric Approach for the Upper Bound Theorem for Minkowski Sums of Convex Polytopes
نویسندگان
چکیده
منابع مشابه
A Geometric Approach for the Upper Bound Theorem for Minkowski Sums of Convex Polytopes
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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15 صفحه اولAn Upper Bound Theorem concerning lattice polytopes
R. P. Stanley proved the Upper Bound Conjecture in 1975. We imitate his proof for the Ehrhart rings. We give some upper bounds for the volume of integrally closed lattice polytopes. We derive some inequalities for the delta-vector of integrally closed lattice polytopes. Finally we apply our results for reflexive integrally closed and order polytopes.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2016
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-016-9818-y