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 an 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.
"Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci." Adv. in Appl. Probab. 44 (2) 391 - 407, June 2012. https://doi.org/10.1239/aap/1339878717