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A269799
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Number of vertices of the fractional perfect matching polytope for the complete graph on n vertices.
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0
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OFFSET
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1,4
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COMMENTS
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The fractional perfect matching polytope of a graph is the set of nonnegative edge weights such that the sum of the weights of the edges incident with any given vertex equals 1.
Sequence up to n=10 computed with PORTA (see links) by Pontus von Brömssen in December 2010.
a(n) equals the number of facets of the polytope P_n defined in Eickmeyer and Yoshida (2008), at least up to n=10.
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LINKS
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Thomas Christof, Sebastian Schenker, PORTA, Ruprecht-Karls-Universität Heidelberg.
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EXAMPLE
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For n=4 the fractional perfect matching polytope is the convex hull of the 3 perfect matchings of K_4, so a(4)=3. For n=6, in addition to the 15 perfect matchings of K_6, the 10 pairs of disjoint triangles with edge weights 1/2 are vertices of the polytope, so a(6)=25.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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