  It is well known that rather general mutation-recombination models can be
solved algorithmically (though not in closed form) by means of Haldane
linearization. The price to be paid is that one has to work with a multiple
tensor product of the state space one started from.
  Here, we present a relevant subclass of such models, in continuous time, with
independent mutation events at the sites, and crossover events between them. It
admits a closed solution of the corresponding differential equation on the
basis of the original state space, and also closed expressions for the linkage
disequilibria, derived by means of M\"obius inversion. As an extra benefit, the
approach can be extended to a model with selection of additive type across
sites. We also derive a necessary and sufficient criterion for the mean fitness
to be a Lyapunov function and determine the asymptotic behaviour of the
solutions.
