Combinatorics of geometrically distributed random variables: Inversions and a parameter of Knuth

Helmut Prodinger

paper

Combinatorics of geometrically distributed random variables: Inversions and a parameter of Knuth

arXiv:math/9903149

Abstract

For words of length $n$ , generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, $q$ --analogues for these parameters from the usual permutation model are obtained.