The hypermetric cone on 8 vertices and some generalizations

2015/03/16 by Michel Deza, Deza, Michel, Mathieu Dutour Sikirić +1
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #math.MG

paper · pdf · doi:10.48550/arxiv.1503.04554

14 pages

arxiv created 2015/03/16 · arxiv updated 2015/03/17

Abstract

The lists of facets -- 298,592 in 86 orbits -- and of extreme rays -- 242,695,427 in 9,003 orbits -- of the hypermetric cone HYP₈ are computed. The first generalization considered is the hypermetric polytope HYPP_n for which we give general algorithms and a description for n≤ 8. Then we shortly consider generalizations to simplices of volume higher than 1, hypermetric on graphs and infinite dimensional hypermetrics.

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