On the exact maximum complexity of Minkowski sums of polytopes (Q1042457)
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scientific article; zbMATH DE number 5646268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the exact maximum complexity of Minkowski sums of polytopes |
scientific article; zbMATH DE number 5646268 |
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On the exact maximum complexity of Minkowski sums of polytopes (English)
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14 December 2009
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It is shown that, if \(P_1, \dots, P_k\) are 3-dimensional convex polytopes lying in \(\mathbb R^3\) and if, for \(1\leq i \leq k\), \(m_i\) is the number of facets of \(P_i\), then the number of facets of the Minkowski sum \(P_1 + \cdots + P_k\) is at most \(4\sum_{1\leq i<j \leq k}m_im_j - (10k-11)\sum_{1\leq i \leq k} m_i + 26 {k\choose 2}\). Examples show that this bound can be achieved.
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polyhedra
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Minkowski sums
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Gaussian maps
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complexity
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