An Upper Bound Theorem for Polytope Pairs
| Autor: | P. Kleinschmidt, C. W. Lee, D. Barnette |
|---|---|
| Rok vydání: | 1986 |
| Předmět: |
Convex analysis
Discrete mathematics General Mathematics Polytope Management Science and Operations Research Hyperplane at infinity h-vector Computer Science Applications Combinatorics Simplicial complex Convex polytope Supporting hyperplane Mathematics::Metric Geometry Vertex enumeration problem Mathematics |
| Zdroj: | Mathematics of Operations Research. 11:451-464 |
| ISSN: | 1526-5471 0364-765X |
| DOI: | 10.1287/moor.11.3.451 |
| Popis: | Assume P* is a simple, convex, d-polytope with ν facets, and F* is a simple, convex d′-polytope with ν′ facets, where 0 ≤ d′ ≤ d − 1. If F* is in fact a face of P* we call (P*, F*) a polytope pair of type (d, ν, d′, ν′). Define Q* to be P* ∼ F*, the unbounded, simple d-polyhedron obtained by applying a protective transformation that sends a supporting hyperplane for F* onto the hyperplane at infinity. In this paper we answer the question: What are the maximum possible numbers of faces of different dimensions that P* and Q* can have? We restate and solve the problem in a dual, simplicial context. |
| Databáze: | OpenAIRE |
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