Injective Convex Polyhedra

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• 作者：Maël Pavón
• 关键词：Convex polyhedra ; Linear programming ; Helly property ; Injectivity ; Hyperconvexity ; Binary intersection property ; Absolute 1 ; Lipschitz retracts
• 刊名：Discrete and Computational Geometry
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：56
• 期：3
• 页码：592-630
• 全文大小：1,326 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Computational Mathematics and Numerical Analysis
  
• 出版者：Springer New York
• ISSN：1432-0444
• 卷排序：56

文摘

We characterize the convex polyhedra P in \({\mathbb {R}}^n\) for which any family of n-dimensional axis-parallel hypercubes centered in P and intersected with P has the binary intersection property. The characterization is effective, concrete and convex geometric. As an application, we prove that the convex polyhedra determined by a finite linear system of inequalities with at most two variables per inequality are of this type. This provides in particular new examples of injective (or equivalently hyperconvex) metric spaces.