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On the Generating Function for Permutations with Repetitions and Inversions

Published online by Cambridge University Press:  20 November 2018

Morton Abramson
Morton Abramson*
Affiliation:
York University, Toronto, Ontario
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Let (a1, a2, …, am), ai ∊ {l, 2, …, n}, be an m-permutation of n (repetitions allowed) with exactly kj of the a's equal to j, j = 1, 2, …, n, m = k1+ …+kn, fixed nonnegative integers. An inversion is a pair i, j such that i < j, ai > aj. Denote by N(r; k, …, kn) the number of such permutations with exactly r inversions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 101 - 102
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Carlitz, L., Sequences and inversions, Duke Math. J. 37 (1970), 193-198.Google Scholar
2. Djokovic, D. Z., Solution to Aufgabe 558, Elemente der Mathematik, 23 (1968), p. 114; Proposer, Heinz Lüneburg, Elemente der Mathematik 22 (1967).Google Scholar