Let b(n;k) denote the number of permutations of f1;:::;ng 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 !f or a range of k including the maximum of the b(n;k)=n!. AMS Subject Classication: 05A16, 05A15, 05A10
['Lane Clark']
An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions