  An expansion of row Markov matrices in terms of matrices related to
permutations with repetitions, is introduced.It generalises the Birkhoff-von
Neumann expansion of doubly stochastic matrices in terms of permutation
matrices (without repetitions).An interpretation of the formalism in terms of
sequences of integers that open random safes described by the Markov matrices,
is presented. Various quantities that describe probabilities and correlations
in this context, are discussed. The Gini index is used to quantify the sparsity
(certainty) of various probability vectors. The formalism is used in the
context of multipartite quantum systems with finite dimensional Hilbert space,
which can be viewed as quantum permutations with repetitions or as quantum
safes. The scalar product of row Markov matrices, the various Gini indices,
etc, are novel probabilistic quantities that describe the statistics of
multipartite quantum systems. Local and global Fourier transforms are used to
define locally dual and also globally dual statistical quantities. The latter
depend on off-diagonal elements that entangle (in general) the various
components of the system. Examples which demonstrate these ideas are also
presented.
