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  • Titel
    Splitting polytopes
  • Verfasser
    Herrmann, Sven ; Joswig, Michael
  • Enthalten in
    Münster Journal of Mathematics, H. Münster Journal of Mathematics, S. 109-142
  • Erschienen
    2008
  • Sprache
    Englisch
  • Dokumenttyp
    Aufsatz in einer Zeitschrift
  • URN
    urn:nbn:de:hbz:6-43529463487 
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Abstract
  • A split of a polytope P is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of P admits a unique decomposition as a linear combination of weight functions corresponding to the splits of P (with a split prime remainder). This generalizes a result of Bandelt and Dress [Adv. Math. 92 (1992)] on the decomposition of finite metric spaces. Introducing the concept of compatibility of splits gives rise to a finite simplicial complex associated with any polytope P, the split complex of P. Complete descriptions of the split complexes of all hypersimplices are obtained. Moreover, it is shown that these complexes arise as subcomplexes of the tropical (pre-)Grassmannians of Speyer and Sturmfels [Adv. Geom. 4 (2004)].
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