Unimodular Triangulations and Coverings of Configurations Arising from Root Systems

Authors:
Hidefumi Ohsugi;Takayuki Hibi
Affiliations:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan. ohsugi@math.sci.osaka-u.ac.jp;Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan. hibi@math.sci.osaka-u.ac.jp
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2001

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Abstract

Existence of a regular unimodular triangulation of the configuration \Phi^+ \cup\,\{ (0, 0,\,{\ldots}\,, 0 ) \} in {\tt R}^n, where Φ+ is the collection of the positive roots of a root system \Phi\,{\subset}\,{\tt R}^n and where (0, 0,\,{\ldots}\,, 0 ) is the origin of {\tt R}^n, will be shown for Φ = Bin, Cin, Din and BCin. Moreover, existence of a unimodular covering of a certain subconfiguration of the configuration Ain+1+ will be studied.