f-vectors of Minkowski additions of convex polytopes

被引：18

作者：

Fukuda, Komei ^{[1
]}

Weibel, Christophe ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, Inst Math, Lausanne, Switzerland

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2007年 / 37卷 / 04期

关键词：

Normal Cone; Discrete Comput Geom; Face Lattice; Convex Polytopes; Moment Curve;

D O I：

10.1007/s00454-007-1310-2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of the face lattice of the sum in terms of the face lattice of a given perfectly centered polytope. Exact face counting formulas are then obtained for perfectly centered simplices and hypercubes. The second type of results concerns tight upper bounds for the f-vectors of Minkowski sums of several polytopes.

引用

页码：503 / 516

页数：14

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