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Encyclopedia of Combinatorial Polytope Sequences



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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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