Oriented matroid polytopes and polyhedral fans are signable

  • Peter Kleinschmidt
  • Shmuel Onn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 920)


While convex polytopes are well known to be shellable, an outstanding open question, of which the answer is likely to be negative, is whether the strictly larger classes of oriented matroid polytopes and polyhedral cone fans are also shellable. In this article we show in a unified way that both classes posses the somewhat weaker property of signability. In particular, this allows us to conclude that simplicial oriented matroid polytopes and fans are partitionable, and to prove they satisfy McMullen's upper bound theorem on the number of faces. We also discuss computational complexity aspects of signability and shellability, and pose questions regarding the hierarchy of signable and shellable complexes.


Simplicial Complex Face Lattice Oriented Matroid Barycentric Subdivision Real Projective Plane 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Peter Kleinschmidt
    • 1
  • Shmuel Onn
    • 2
  1. 1.Wirtschaftswissenschaftliche Fakultät, Lehrstuhl für WirtschaftsinformatikUniversität PassauPassauGermany
  2. 2.Department of Operations ResearchSchool of Industrial Engineering and Management, TechnionHaifaIsrael

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