A combinatorial proof of the log-concavity of the numbers of permutations with $k$ runs

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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.
10 pages, 4 figures

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Combinatorics, O5A15

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http://salesiana.dossiersoluciones.com/handle/123456789/78046

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9902020
 http://arxiv.org/abs/math/9902020

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arXiv