The Hypermetric Cone Is Polyhedral

  title={The Hypermetric Cone Is Polyhedral},
  author={M. DEZA},
  • M. DEZA
  • Published 1993
The hypermetric cone Hn is the cone in the space R n(n1)/2 of all vectors d = (dij) 1 <i< j <_ n satisfying the hypermetric inequalities: El<_i<j<n zjzjdij ~0 for all integer vectors z in Z n with E l < i < n zi = 1. We explore connections of the hypermetric cone with quadratic forms and the geometry of numbers (empty spheres and L-polytopes in lattices). As an application, we show that the hypermetric cone Hn is polyhedral. 

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