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

Mathematics – Combinatorics

Scientific paper

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Scientific paper

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.

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