From equations (32) and (35), we prove that the (unique) solution of the recursion relation (30) is given by equation (23), Q i = R 1 + R 2 + ,

Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process, Phys. Rev. E, vol.69, p.66136, 2004. ,

An exactly soluble non-equilibrium system: the asymmetric simple exclusion process, Phys. Rep, vol.301, p.65, 1998. ,

Hidden symmetries in the one-dimensional antiferromagnetic Heisenberg model, Phys. Rev. B, vol.42, p.4656, 1990. ,

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics, J. Phys. A: Math. Gen, vol.39, p.12679, 2006. ,

Family of Commuting Operators for the Totally Asymmetric Exclusion Process, Submitted to, J. Phys. A: Math. Theor, 2007. ,

An exactly solvable anisotropic directed percolation model in three dimensions, Phys. Rev. Lett, vol.81, p.1646, 1998. ,

The asymmetric exclusion model with sequential update, J. Phys. A: Math. Gen, vol.29, p.305, 1996. ,

Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process, J. Stat. Phys, vol.118, p.511, 2005. ,

Exactly solvable models for many-body systems far from equilibrium in, Phase Transitions and Critical Phenomena, vol.19, 2001. ,

Large scale dynamics of interacting particles, 1991. ,