Geodesic
The number of inversions in permutations: A saddle point approach
Journal of integer sequences, Tome 6 (2003) no. 2
Using the saddle point method, we obtain from the generating function of the inversion numbers of permutations and Cauchy's integral formula asymptotic results in central and noncentral regions.
Classification : 05A16, 05A10
Keywords: inversions, permutations, saddle point method 
@article{JIS_2003__6_2_a5,
     author = {Louchard,  Guy and Prodinger,  Helmut},
     title = {The number of inversions in permutations: {A} saddle point approach},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {2},
     zbl = {1024.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_2_a5/}
}
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Louchard,  Guy; Prodinger,  Helmut. The number of inversions in permutations: A saddle point approach. Journal of integer sequences, Tome 6 (2003) no. 2. http://geodesic.mathdoc.fr/item/JIS_2003__6_2_a5/