No formula with denominators of bounded degree, in the total mutation parameter or in rho, for the two-locus sampling recursion
This entry formalizes results on the degree of denominators of any closed-form expression for the solution of the two-locus sampling recursion of the coalescent with recombination, with two alleles at each locus and parent-independent mutation. The mutation rates, the recombination rate rho, and the allele frequencies are independent indeterminates, and the recursion is solved over a field of rational functions in them. An expression is built from rational constants, arbitrary coefficients from the coefficient field, the rates, sums, products, and quotients; it is admissible at degree D when…
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