Titlebook: Geometry of Cuts and Metrics; Michel Marie Deza,Monique Laurent Book 1997 Springer-Verlag Berlin Heidelberg 1997 Geometrie von Polyedern.G

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Delaunay Polytopes: Rank and Hypermetric Facese hypermetric cone. This notion of rank for a Delaunay polytope . has the following geometric interpretation: It coincides with the number of degrees of freedom one has when deforming . in such a way that the deformed polytope remains a Delaunay polytope; a precise formulation can be found in Theorem 15.2.5.

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defeatist

Preliminaries on Distancesidean case . = 2 and the semimetric case . = ∞. We will consider the general case . ≥ 1 only episodically. However, we now introduce the definitions for . arbitrary, as this permits us to have a unified setting for the various parameters and, moreover, to emphasize the specificity of the case . = 1.

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Horizon

,-Metrics from Lattices, Semigroups and Normed Spacesven with a sketch of proof only or, at times, with no proof at all. They indeed rely on analytical methods whose exposition is beyond the scope of this book. We do, however, provide references that the interested reader may consult for further information.

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Examples of the Use of the ,,-Metric the ..-metric is illustrated, in particular, by the great variety of names under which it is known. For example, the Manhattan metric, the taxi-cab metric, or the 4-metric are different names for the same notion, namely, the ℓ. distance in the plane; more terminology is given in Section 12.3.

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0937-5511 nections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc...This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new

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