The Discrete and Continuous Painleve VI Hierarchy and the Garnier   Systems
  We present a general scheme to derive higher-order members of the Painleve VI (PVI) hierarchy of ODE's as well as their difference analogues. The derivation is based on a discrete structure that sits on the background of the PVI equation and that consists of a system of partial difference equations on a multidimensional lattice. The connection with the isomonodromic Garnier systems is discussed. 
F.W. Nijhoff and A.J. Walker