This material has been published in
J. Combin. Theory Ser. A
74 (1996), 351-354,
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Christian Krattenthaler
Combinatorial proof of the log-concavity of the
sequence of matching numbers
(4 pages)
Abstract.
For k>=l we construct an injection from the set of
pairs of matchings in a given graph G of sizes l-1 and k+1 into
the set of pairs of matchings in G of sizes l and k. This
provides a combinatorial proof of the log-concavity of the sequence
of matching numbers of a graph. Besides, this injection implies that
a certain weighted version of the matching numbers is strongly
x-log-concave in the sense of Sagan (Discrete Math. 99 (1992),
289-306).
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