An upper bound on the denominators of solutions of the two-locus sampling recursion
This entry formalizes degree and divisibility facts about the denominators of solutions to the two-locus sampling recursion with two alleles at each locus. Centred moments of a solution, grouped in blocks by the numbers i and j of lineages at the two loci, satisfy a tridiagonal linear system with matrix T(i, j) whose right-hand side involves only smaller blocks. An explicit product D of linear factors in the mutation rates and of block determinants E(p, s) = det T(p, s) clears the denominator of the solution: D times the solution lies in any subring that contains the parameters.…
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