Arithmetic Discrete Hyperspheres and Separatingness

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• 作者：Christophe Fiorio ; Jean-Luc Toutant
• 刊名：Lecture Notes in Computer Science
• 出版年：2006
• 出版时间：2006
• 年：2006
• 卷：4245
• 期：1
• 页码：425-436
• 全文大小：373 KB
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

In the framework of the arithmetic discrete geometry, a discrete object is provided with its own analytical definition corresponding to a discretization scheme. It can thus be considered as the equivalent, in a discrete space, of a Euclidean object. Linear objects, namely lines and hyperplanes, have been widely studied under this assumption and are now deeply understood. This is not the case for discrete circles and hyperspheres for which no satisfactory definition exists. In the present paper, we try to fill this gap. Our main results are a general definition of discrete hyperspheres and the characterization of the k-minimal ones thanks to an arithmetic definition based on a non-constant thickness function. To reach such topological properties, we link adjacency and separatingness with norms.