Journal of Integer Sequences, Vol. 6 (2003), Article 03.2.8

The Number of Inversions in Permutations: A Saddle Point Approach


Guy Louchard
Département d'Informatique
CP 212, Boulevard du Triomphe
B-1050 Bruxelles
Belgium

Helmut Prodinger
University of the Witwatersrand
The John Knopfmacher Centre for Applicable Analysis and Number Theory
School of Mathematics
P. O. Wits
2050 Johannesburg
South Africa

Abstract: 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.

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Received November 15, 2002; revised version received July 3, 2003. Published in Journal of Integer Sequences July 22, 2003.

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