Discrete hyperbolic geometry

Abstract

The aim of the paper is to make geometers and combinatorialists familiar with old and new connections between the geometry of Lorentz space and combinatorics. Among the topics treated are equiangular lines and their relations to spherical 2-distance sets; spherical and hyperbolic root systems and their relation to graphs whose second largest eigenvalue does not exceed one or two, respectively; and work of Niemeier, Vinberg, Conway and Sloane on Euclidean and Lorentzian unimodular lattices.

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The first author gratefully acknowledges the support of the Dutch organization for pure research, Z. W. O., during Sept.—Dec. 1980, thus allowing him to spend four months in Eindhoven (Netherlands).

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Neumaier, A., Seidel, J.J. Discrete hyperbolic geometry. Combinatorica 3, 219–237 (1983). https://doi.org/10.1007/BF02579296

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AMS subject classification (1980)

  • 51 M 10
  • 05 C 35