  Full counting statistics concerns the stochastic transport of electrons in
mesoscopic structures. Recently it has been shown that the charge transport
statistics for non-interacting electrons in a two-terminal system is always
generalized binomial: it can be decomposed into independent single-particle
events and the zeros of the generating function are real and negative. Here we
investigate how the zeros of the generating function move into the complex
plane due to interactions and demonstrate that the positions of the zeros can
be detected using high-order factorial cumulants. As an illustrative example we
consider electron transport through a Coulomb blockade quantum dot for which we
show that the interactions on the quantum dot are clearly visible in the
high-order factorial cumulants. Our findings are important for understanding
the influence of interactions on counting statistics and the characterization
in terms of zeros of the generating function provides us with a simple
interpretation of recent experiments, where high-order statistics have been
measured.
