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The classification of finite connected hypermetric spaces

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Abstract

A finite distance spaceX, d d: X 2 → ℤ is hypermetric (of negative type) if ∑a x a y d(x, y) ≤ 0 for all integral sequences{a x ∣x ∈ X} that sum to 1 (sum to 0).X, d is connected if the set {(x, y)∣d(x, y) = 1, x, y ∈ X} is the edge set for a connected graph onX, and graphical ifd is the path length distance for this graph. Then we prove

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    Paul Terwilliger

  2. Centre National de la Recherche Scientifique, 75007, Paris, France

    Michel Deza

  3. Department of Mathematical Engineering, University of Tokyo, 113, Tokyo, Japan

    Michel Deza

Authors
  1. Paul Terwilliger
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  2. Michel Deza
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The first author was partially supported by NSF grant DMS 8600882.

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Terwilliger, P., Deza, M. The classification of finite connected hypermetric spaces. Graphs and Combinatorics 3, 293–298 (1987). https://doi.org/10.1007/BF01788552

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  • DOI: https://doi.org/10.1007/BF01788552

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