A combinatorial proof of the log-concavity of the numbers of permutations with k runs
Miklós Bóna, Richard Ehrenborg
Abstract
We combinatorially prove that the number R(n,k) of permutations of length n having k runs is a log-concave sequence in k, for all n. We also give a new combinatorial proof for the log-concavity of the Eulerian numbers.
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