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Birkhoff polytope
 (No 3d term.) [polymake for n=3] |
• Birkhoff polytopes B [wiki] • assignment polytope • Transportation polytope Trans_n(1, 1, . . . , 1) [arxiv] (Mészáros, Morales, Rhoades) • perfect matching polytope of complete bipartite graph • set of doubly stochastic matrices • convex_hull({M | M an nxn permutation matrix}) |
• Dimensions: 0, 1, 4, 9, 16 ... (n-1)^2 • Number of Vertices in nth polytope: 1, 2, 6, 24, ... n! [ OEIS A000142] • Number of Facets: 0, 2, 9, 16,... n^2 [ OEIS A000290] • f-vectors: 1, 2, 1, 6, 15, 18, 9, 1 ... [ OEIS ?] |
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