Geodesic
A combinatorial proof of the log-concavity of a famous sequence counting permutations
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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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.
DOI : 10.37236/1889
Classification : 05A05, 05A15
Mots-clés : log-concavity, inversion number of permutations, non-generating function proof 
@article{10_37236_1889,
     author = {Mikl\'os B\'ona},
     title = {A combinatorial proof of the log-concavity of a famous sequence counting permutations},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1889},
     zbl = {1067.05002},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1889/}
}
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Miklós Bóna. A combinatorial proof of the log-concavity of a famous sequence counting permutations. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1889

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