  The deterministic selection-recombination equation describes the evolution of
the genetic type composition of a population under selection and recombination
in a law of large numbers regime. So far, an explicit solution has seemed out
of reach; only in the special case of three sites with selection acting on one
of them has an approximate solution been found, but without an obvious path to
generalisation. We use both an analytical and a probabilistic, genealogical
approach for the case of an \emph{arbitrary} number of neutral sites linked to
one selected site. This leads to a recursive integral representation of the
solution. Starting from a variant of the ancestral selection-recombination
graph, we develop an efficient genealogical structure, which may, equivalently,
be represented as a weighted partitioning process, a family of Yule processes
with initiation and resetting, and a family of initiation processes. We prove
them to be dual to the solution of the differential equation forward in time
and thus obtain a stochastic representation of the deterministic solution,
along with the Markov semigroup in closed form.
