{"id":"palomar/PALOMAR-2026-10-29-000024","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000024-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["math.AC","q-bio.PE","msc:12E05","msc:92D10","msc:13P15"],"score":0,"title":"No formula with denominators of bounded degree, in the total mutation parameter or in rho, for the two-locus sampling recursion","trust":"high","domain":"math.AC","source":"palomar","authors":["X. Lee","N. Volkov"],"reviews":0,"subject":"math.AC","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true}