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An explicit block-recursive formula for solutions of the two-locus sampling recursion

X. Lee, N. Volkov

Palomar Registrypalomar/PALOMAR-2026-10-29-000017Oct 29, 2026q-bio.PEscore 0

This entry formalizes an explicit block-recursive formula for the solution of the two-locus sampling recursion under parent-independent mutation, with two alleles at each locus, positive mutation rates, and nonnegative recombination rate, over any ordered field. The explicit expression equals every solution of the recursion and is itself a solution, so it is the unique solution. Lumping statements show that merging alleles, by pushing configurations forward along maps between allele sets of any sizes, carries solutions to solutions, and that when every allele class is merged into two classes…

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