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

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

1999-02-03

arxiv.org/abs/math/9902020v1

Mathematics

Combinatorics

10 pages, 4 figures

Scientific paper

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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