Journal of Integer Sequences, Vol. 4 (2001), Article 01.1.4

Permutations with Inversions

Barbara H. Margolius

Cleveland State University
Cleveland, Ohio 44115

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Abstract: The number of inversions in a random permutation is a way to measure the extent to which the permutation is ``out of order''. Let In(k) denote the number of permutations of length n with k inversions. This paper gives asymptotic formulae for the sequences {In+k(n), n=1,2,...} for fixed k.

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(Concerned with sequences A000707 A001318 A001892 A001893 A001894 A005283 A005284 A005285 A008302.)

Received May 30, 2001; revised version received July 9, 2001. Published in Journal of Integer Sequences, November 8, 2001.

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