Geodesic
An asymptotic expansion for the number of permutations with a certain number of inversions
The electronic journal of combinatorics, Tome 7 (2000)
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Let $b(n,k)$ denote the number of permutations of $\{1,\ldots,n\}$ with precisely $k$ inversions. We represent $b(n,k)$ as a real trigonometric integral and then use the method of Laplace to give a complete asymptotic expansion of the integral. Among the consequences, we have a complete asymptotic expansion for $b(n,k)/n!$ for a range of $k$ including the maximum of the $b(n,k)/n!$.
DOI : 10.37236/1528
Classification : 05A16, 05A15, 05A10
Mots-clés : number of permutations, inversions, asymptotic expansion 
@article{10_37236_1528,
     author = {Lane Clark},
     title = {An asymptotic expansion for the number of permutations with a certain number of inversions},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1528},
     zbl = {0969.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1528/}
}
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%0 Journal Article
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%T An asymptotic expansion for the number of permutations with a certain number of inversions
%J The electronic journal of combinatorics
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Lane Clark. An asymptotic expansion for the number of permutations with a certain number of inversions. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1528

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