  Linear rate equations are used to describe the cascading decay of an initial
heavy cluster into fragments. This representation is based upon a triangular
matrix of transition rates. We expand the state vector of mass multiplicities,
which describes the process, into the biorthonormal basis of eigenmodes
provided by the triangular matrix. When the transition rates have a scaling
property in terms of mass ratios at binary fragmentation vertices, we obtain
solvable models with explicit mathematical properties for the eigenmodes. A
suitable continuous limit provides an interpolation between the solvable
models. It gives a general relationship between the decay products and the
elementary transition rates.
