Abstract
Existence of a regular unimodular triangulation of the configuration \(\Phi ^ + \cup \{ (0,0,...,0)\} {\text{ in }}R^n\), where Φ+ is the collection of the positive roots of a root system \(\Phi \subset R^n \) and where (0, 0,...,0 ) is the origin of \(R^n \), will be shown for Φ = B n , C n , D n and BC n . Moreover, existence of a unimodular covering of a certain subconfiguration of the configuration A n+1 + will be studied.
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Ohsugi, H., Hibi, T. Unimodular Triangulations and Coverings of Configurations Arising from Root Systems. Journal of Algebraic Combinatorics 14, 199–219 (2001). https://doi.org/10.1023/A:1012772002661
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DOI: https://doi.org/10.1023/A:1012772002661