2007/08/06 by Mathieu Dutour Sikirić, Mathieu Dutour Sikiric, Sikiric, Mathieu Dutour +2
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Polynomial and algebraic computation #math.CO #math.MG
paper · pdf · doi:10.48550/arxiv.0708.0747
20 pages 2 figures, 2 tables
openalex publication_date 2007/08/06 · arxiv created 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hypermetric cone \HYPn+1 is the parameter space of basic Delaunay polytopes in n-dimensional lattice. The cone \HYPn+1 is polyhedral; one way of seeing this is that modulo image by the covariance map \HYPn+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 \HYPn+1 of hypermetrics on n+1 points contains exactly 1/2n! principal L-domains. We give a detailed description of the decomposition of \HYPn+1 for n=2,3,4 and a computer result for n=5 (see Table \refTableDataHYPn). Remarkable properties of the root system D4 are key for the decomposition of \HYP5.