Oriented matroid polytopes and polyhedral fans are signable
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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.
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- Oriented matroid polytopes and polyhedral fans are signable
- Book Title
- Integer Programming and Combinatorial Optimization
- Book Subtitle
- 4th International IPCO Conference Copenhagen, Denmark, May 29–31, 1995 Proceedings
- pp 198-211
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Author Affiliations
- 1. Wirtschaftswissenschaftliche Fakultät, Lehrstuhl für Wirtschaftsinformatik, Universität Passau, 94030, Passau, Germany
- 2. Department of Operations Research, School of Industrial Engineering and Management, Technion, 32000, Haifa, Israel
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