Arithmetic Discrete Hyperspheres and Separatingness [chapter]

Christophe Fiorio, Jean-Luc Toutant
2006 Lecture Notes in Computer Science  
In the framework of 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 an 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
more » ... try to fill this gap. Our main result is the characterization of the k-minimal discrete hypersphere thanks to an arithmetic definition based on a non-constant thickness function. To reach such a topological property, we link adjacency and separability with norms.
doi:10.1007/11907350_36 fatcat:qpwpuxusvvfptp76aoe2ukzsg4