

A269799


Number of vertices of the fractional perfect matching polytope for the complete graph on n vertices.


0




OFFSET

1,4


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..10.
Roger E. Behrend, Fractional perfect bmatching polytopes I: General theory, Linear Algebra and its Applications 439 (2013), 38223858.
Thomas Christof, Sebastian Schenker, PORTA, RuprechtKarlsUniversität Heidelberg.
K. Eickmeyer and R. Yoshida, The Geometry of the NeighborJoining Algorithm for Small Trees, in: Proc. 3rd Int. Conference on Algebraic Biology, 2008, Castle of Hagenberg, Austria, Springer LNCS5147, arXiv:0908.0098 [math.CO], 2009.


EXAMPLE

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.


CROSSREFS

Cf. A123023.
Sequence in context: A072398 A134924 A042547 * A079039 A209987 A332095
Adjacent sequences: A269796 A269797 A269798 * A269800 A269801 A269802


KEYWORD

nonn,more


AUTHOR

Pontus von Brömssen, Mar 05 2016


STATUS

approved



