A Combinatorial Proof of the Log-Concavity of a Famous Sequence Counting Permutations

Miklós Bóna

Abstract


We provide a combinatorial proof for the fact that for any fixed $n$, the sequence $\{i(n,k)\}_{0\leq k\leq {n\choose 2}}$ of the numbers of permutations of length $n$ having $k$ inversions is log-concave.


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