Encyclopedia of Combinatorial Polytope Sequences

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Perfect Matching polytope of complete graph

(No 3d term.) [polymake for 2n=6] |
• Perfect Matching polytope of complete graph on 2n nodes PM(n) = PM(K_2n) [wiki]
• convex_hull({ incidence_vector_PM | PM a perfect matching of the complete graph on 2n nodes}) [PNAS](P.Diaconis, S. Holmes) |
• Dimensions: 0, 2, 9, ... • Number of Vertices in nth polytope:1, 3, 15, 105, ... (2n-1)!! [ OEIS A001147]• Number of Facets: 0, 3, 25, ... OPEN [ OEIS ?] • f-vectors: 1, 3, 3, 1, 15, 105, 435, 1095, 1657, 1470, 735, 195, 25, 1, ... [ OEIS ?] |