The decomposition of the hypermetric cone into L-domains

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dc.creatorSikiric, Mathieu Dutour
dc.creatorGrishukhin, Viatcheslav
dc.date2007-08-06
dc.date2008-08-11
dc.date.accessioned2026-07-07T09:55:33Z
dc.date.available2026-07-07T09:55:33Z
dc.descriptionThe hypermetric cone $\HYP_{n+1}$ is the parameter space of basic Delaunay polytopes in n-dimensional lattice. The cone $\HYP_{n+1}$ is polyhedral; one way of seeing this is that modulo image by the covariance map $\HYP_{n+1}$ is a finite union of L-domains, i.e., of parameter space of full Delaunay tessellations. In this paper, we study this partition of the hypermetric cone into L-domains. In particular, it is proved that the cone $\HYP_{n+1}$ of hypermetrics on n+1 points contains exactly {1/2}n! principal L-domains. We give a detailed description of the decomposition of $\HYP_{n+1}$ for n=2,3,4 and a computer result for n=5 (see Table \ref{TableDataHYPn}). Remarkable properties of the root system $\mathsf{D}_4$ are key for the decomposition of $\HYP_5$.
dc.description20 pages 2 figures, 2 tables
dc.identifierhttps://arxiv.org/abs/0708.0747
dc.identifierhttp://arxiv.org/abs/0708.0747
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166669
dc.subjectCombinatorics
dc.subjectMetric Geometry
dc.titleThe decomposition of the hypermetric cone into L-domains
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