{"id":"palomar/PALOMAR-2026-10-29-000026","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000026-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["q-bio.PE","math.CO","msc:92D10","msc:60C05","msc:05A18","msc:60J90"],"score":0,"title":"A partition-pair decomposition of the two-locus sampling probability with Ewens marginals","trust":"high","domain":"q-bio.PE","source":"palomar","authors":["X. Lee","N. Volkov"],"reviews":0,"subject":"q-bio.PE","summary":"This entry formalizes a decomposition of the two-locus sampling probability, under finite-allele parent-independent mutation, in terms of pairs of set partitions of the sample, with Ewens marginals at each locus. A partition-carrying ancestral process with coalescence, mutation, and recombination records, at each locus, which sample members lose their ancestry to the same mutation; the kernel is the probability that it ends with a given pair of partitions. The solution of the two-locus sampling recursion at a fully typed sample is the sum over pairs of partitions of the kernel times the…","category":"research","comments":0,"disputed":false,"division":"q-bio","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true}