  A hierarchical system of equations is introduced to describe dynamics of
`sizes' of infinite clusters which coagulate and fragmentate with homogeneous
rates of certain form. We prove that this system of equations is solved weakly
by correlation measures for stochastic dynamics of interval partitions evolving
according to some split-merge transformations. Regarding those processes, a
sufficient condition for a distribution to be reversible is given. Also, an
asymptotic result for properly rescaled processes is shown to obtain a solution
to a nonlinear equation called the coagulation-fragmentation equation.
