{"id":"palomar/PALOMAR-2026-10-29-000012","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000012-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["q-bio.PE","math.PR","msc:92D10","msc:60C05","msc:05A17","msc:60J10"],"score":0,"title":"The Ewens sampling formula and its generative urn","trust":"high","domain":"q-bio.PE","source":"palomar","authors":["X. Lee","N. Volkov"],"reviews":0,"subject":"q-bio.PE","summary":"This entry formalizes the Ewens sampling formula for partitions of n and its relation to a generative urn. Over any field of characteristic zero, the weights sum to 1 whenever the rising factorial in θ is nonzero, and they have an explicit product form in the part counts. For θ > 0 the urn law on partitions of n equals the Ewens weights. The conditional law given the number of parts is expressed through Stirling numbers of the first kind, and the weights are consistent under deletion of one sampled individual.","category":"research","comments":0,"disputed":false,"division":"q-bio","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true,"formalizes":[{"title":"The sampling theory of selectively neutral alleles","identifier":"doi:10.1016/0040-5809(72)90035-4","relationship":"formalizes"},{"title":"Probability Models for DNA Sequence Evolution","identifier":"doi:10.1007/978-0-387-78168-6","relationship":"formalizes"},{"title":"Polya-like urns and the Ewens' sampling formula","identifier":"doi:10.1007/BF00275863","relationship":"adapts"},{"title":"Random partitions in population genetics","identifier":"doi:10.1098/rspa.1978.0089","relationship":"formalizes"}]}