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Symmetric Path Polytope
 (No 3d term) [polymake for n=4,5] |
• s-t Path Polytopes of complete graph Path(n)= Path(K_n), n>1 [Springer] (A. Schrijver) • convex_hull({incidence_vector_F | F a path from node s to node t of the complete graph on n nodes}) |
• Dimensions: 0, 1, 4, 8,... conject. (n choose 2)-2 [ OEIS A034856] • Number of Vertices in nth polytope: 1, 2, 5, 16, 65, ... Sum_{k=0..(n-2)} (n-2)!/k! [ OEIS A000522] • Number of Facets: 2, 5, 25, ... OPEN [ OEIS ?] • f-vectors: 1, 2, 1, 5, 10, 10, 5, 1, 16, 102, 334, 622, 685, 442, 156, 25, 1... [ OEIS ?] |
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