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Pitters, Philip Weissmann","submitted_at":"2019-06-14T10:27:40Z","abstract_excerpt":"Consider a random permutation of $\\{1, \\ldots, \\lfloor n^{t_2}\\rfloor\\}$ drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$ denote the number of its cycles, where $t\\equiv (t_1, t_2)\\in\\mathbb [0, 1]^2$.\n  Next, consider a sample drawn from a large, neutral population of haploid individuals subject to mutation under the infinitely many sites model of Kimura whose genealogy is governed by Kingman's coalescent. Let $S(n, t)$ count the number of segregating sites in a sample of size $\\lfloor n^{t_2}\\rfloor$ when mutations arrive at rate $t_1/2$.\n  We show that $K(n, (t_1/"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.06336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-14T10:27:40Z","cross_cats_sorted":[],"title_canon_sha256":"9e27a649115cf2a9b46c51136e2ebf9f6e1821c6773f5a3151d5a390957c339b","abstract_canon_sha256":"6ad72bdb47ae651ecd06027b858c9a1c64e206dd5e43882f5c1ed2cc0804b686"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:13.967778Z","signature_b64":"cN5YHiOAWpwyz1lUBJ5tuLt8yM7BHEsxtzJjfuZX1CrNkiKZ4lWCSVcaXfcd5mbisY7Ig32Qyyx90Ummwm/eBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9227c8f2417bb65a7f6e986ad86ccb1dd58013bb75431d90f709f8905957baa","last_reissued_at":"2026-05-17T23:43:13.967306Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:13.967306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson limit for the number of cycles in a random permutation and the number of segregating sites","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Helmut H. 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Let $S(n, t)$ count the number of segregating sites in a sample of size $\\lfloor n^{t_2}\\rfloor$ when mutations arrive at rate $t_1/2$.\n  We show that $K(n, (t_1/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06336","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.06336","created_at":"2026-05-17T23:43:13.967389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.06336v1","created_at":"2026-05-17T23:43:13.967389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06336","created_at":"2026-05-17T23:43:13.967389+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ERHZDZEC65W","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ERHZDZEC65WLJ7W","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ERHZDZE","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH","json":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH.json","graph_json":"https://pith.science/api/pith-number/5ERHZDZEC65WLJ7W5GDK3BWMWH/graph.json","events_json":"https://pith.science/api/pith-number/5ERHZDZEC65WLJ7W5GDK3BWMWH/events.json","paper":"https://pith.science/paper/5ERHZDZE"},"agent_actions":{"view_html":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH","download_json":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH.json","view_paper":"https://pith.science/paper/5ERHZDZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.06336&json=true","fetch_graph":"https://pith.science/api/pith-number/5ERHZDZEC65WLJ7W5GDK3BWMWH/graph.json","fetch_events":"https://pith.science/api/pith-number/5ERHZDZEC65WLJ7W5GDK3BWMWH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH/action/storage_attestation","attest_author":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH/action/author_attestation","sign_citation":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH/action/citation_signature","submit_replication":"https://pith.science/pith/5ERHZDZEC65WLJ7W5GDK3BWMWH/action/replication_record"}},"created_at":"2026-05-17T23:43:13.967389+00:00","updated_at":"2026-05-17T23:43:13.967389+00:00"}