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Flow Polytope
 (4, 0, 0, 0) [polymake for n=5,6] |
• Flow Polytopes of complete graph FLOW(n)= F(K_n) [arxiv] (Mészáros, Morales, Striker) • Chan-Robbins-Yuen Polytopes CRY(n-1) • convex_hull({incidence_vector_F | F a unit flow of the complete graph on n nodes}) • Volume equals product of the first n - 2 Catalan numbers |
• Dimensions: 1, 3, 6, 10, 15,... (n-1 choose 2) [ OEIS A000217] • Number of Vertices in nth polytope: 2, 4, 8, 16, 32 ... 2^(n-2) [ OEIS A000079] • Number of Facets: 2, 4, 8, 13 ... OPEN [ OEIS ?] • f-vectors: 1, 2, 1, 4, 6, 4, 1, 8, 26, 45, 45, 26, 8, 1, 16, 98, 327, 681, 944, 897, 588, 262, 76, 13... [ OEIS ?] |
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