  Obtaining a closed-form sampling distribution for the coalescent with
recombination is a challenging problem. In the case of two loci, a new
framework based on asymptotic series has recently been developed to derive
closed-form results when the recombination rate is moderate to large. In this
paper, an arbitrary number of loci is considered and combinatorial approaches
are employed to find closed-form expressions for the first couple of terms in
an asymptotic expansion of the multi-locus sampling distribution. These
expressions are universal in the sense that their functional form in terms of
the marginal one-locus distributions applies to all finite- and
infinite-alleles models of mutation.
