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Linear Ordering Polytope
 (8, 0, 0, 0) |
• Linear order polytopes P_LO [zib.de] (M. Grötschel, M. Jünger, G. Reinelt), [citeseer] (T. Christof, G. Reinelt), [arxiv] (Katthän), [SMAPO library] • Binary choice polytopes • convex_hull({char_vector_LO | LO a linear order with n elements}) |
• Dimensions: 0, 1, 3, 6, 10, ... (n choose 2) • Numbers of vertices in nth polytope: 1, 2, 6, 24, ... n! [ OEIS A000142] • Facets: 0, 2, 8, 20, 40, 910, 87472 ... OPEN [ OEIS ?] • f-vectors: 1, 2, 1, 6, 8, 1, 24, ... [ OEIS ?] |
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