Geometry of Cuts and Metrics

Authors:

ISBN: 978-3-642-04294-2 (Print) 978-3-642-04295-9 (Online)

Table of contents (31 chapters)

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  1. Front Matter

    Pages i-xii

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    Book Chapter

    Pages 1-10

    Outline of the Book

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    Book Chapter

    Pages 11-22

    Basic Definitions

  4. Measure Aspects: ℓ 1-Embeddability and Probability

    1. Front Matter

      Pages 23-26

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      Book Chapter

      Pages 27-35

      Preliminaries on Distances

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      Book Chapter

      Pages 37-52

      The Cut Cone and 1-Metrics

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      Book Chapter

      Pages 53-65

      The Correlation Cone and {0,1}-Covariances

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      Book Chapter

      Pages 67-92

      Conditions for L 1-Embeddability

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      Book Chapter

      Pages 93-104

      Operations

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      Book Chapter

      Pages 105-111

      L 1-Metrics from Lattices, Semigroups and Normed Spaces

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      Book Chapter

      Pages 113-124

      Metric Transforms of L 1-Spaces

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      Book Chapter

      Pages 125-137

      Lipschitz Embeddings

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      Book Chapter

      Pages 139-159

      Dimensionality Questions for 1-Embeddings

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      Book Chapter

      Pages 161-166

      Examples of the Use of the L 1-Metric

  5. Hypermetric Spaces: an Approach via Geometry of Numbers

    1. Front Matter

      Pages 167-174

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      Book Chapter

      Pages 175-192

      Preliminaries on Lattices

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      Book Chapter

      Pages 193-216

      Hypermetrics and Delaunay Polytopes

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      Book Chapter

      Pages 217-233

      Delaunay Polytopes: Rank and Hypermetric Faces

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      Book Chapter

      Pages 235-250

      Extreme Delaunay Polytopes

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      Book Chapter

      Pages 251-273

      Hypermetric Graphs

  6. Isometric Embeddings of Graphs

    1. Front Matter

      Pages 275-278

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      Book Chapter

      Pages 279-281

      Preliminaries on Graphs

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      Book Chapter

      Pages 283-295

      Isometric Embeddings of Graphs into Hypercubes

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      Book Chapter

      Pages 297-311

      Isometric Embeddings of Graphs into Cartesian Products

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