The hypermetric cone is polyhedral |
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Authors: | M Deza V P Grishukhin M Laurent |
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Institution: | (1) Ecole Normale Supérieure, LIENS, 45 Rue d'Ulm, 75230 Paris cedex 05, France;(2) CEMI, Academy of Sciences of Russia, Krasikova 32, 117418 Moscow, Russia |
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Abstract: | The hypermetric coneH
n is the cone in the spaceR
n(n–1)/2 of all vectorsd=(d
ij)1i<jn
satisfying the hypermetric inequalities: –1ijn
z
j
z
j
d
ij
0 for all integer vectorsz inZ
n with –1in
z
i
=1. We explore connections of the hypermetric cone with quadratic forms and the geometry of numbers (empty spheres andL-polytopes in lattices). As an application, we show that the hypermetric coneH
n is polyhedral. |
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Keywords: | 52 A 43 52 A 25 05 A 99 |
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