  Quantum dots are nanoscopic systems, where carriers are confined in all three
spatial directions. Such nanoscopic systems are suitable for fundamental
studies of quantum mechanics and are candidates for applications such as
quantum information processing. It was also proposed that linear arrangements
of quantum dots could be used as quantum cascade laser. In this work we study
the impact of electron-electron interactions on transport in a spinful serial
triple quantum dot system weakly coupled to two leads. We find that due to
electron-electron scattering processes the transport is enabled beyond the
common single-particle transmission channels. This shows that the scenario in
the serial quantum dots intrinsically deviates from layered structures such as
quantum cascade lasers, where the presence of well-defined single-particle
resonances between neighboring levels are crucial for device operation.
Additionally, we check the validity of the Pauli master equation by comparing
it with the first-order von Neumann approach. Here we demonstrate that
coherences are of relevance if the energy spacing of the eigenstates is smaller
than the lead transition rate multiplied by $\hbar$.
