{"id":"palomar/PALOMAR-2026-10-29-000011","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000011-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["math.AC","q-bio.PE","msc:92D10","msc:12E05","msc:13F20"],"score":0,"title":"An upper bound on the denominators of solutions of 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 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.…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true}