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Matching Polytope of complete graph
 (4, 0, 0, 0) [polymake for n=4] |
• Matching Polytopes of complete graph MATCH(n)= M(K_n) [wiki] • convex_hull({incidence_vector_M | M a general matching of the complete graph on n nodes}) [imsc](M. Mahajan) |
• Dimensions: 0, 1, 3, 6, 10, 15,... (n choose 2) [ OEIS A000217] • Number of Vertices in nth polytope: 1, 2, 4, 10, 26, 76, 232, 764... Sum_{k=0..[ n/2 ]} n!/((n-2*k)!*2^k*k!) [ OEIS A000085] • Number of Facets: 2, 4, 14... OPEN [ OEIS ?] • f-vectors: 1, 2, 1, 4, 6, 4, 1, 10, 39, 78, 86, 51, 14,... [ OEIS ?] |
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