{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WAGZQES6P4XXGD3HRMDJKXKDXT","short_pith_number":"pith:WAGZQES6","schema_version":"1.0","canonical_sha256":"b00d98125e7f2f730f678b06955d43bcdeab8d7c3a23719a2db283a06e06a87e","source":{"kind":"arxiv","id":"1601.06991","version":2},"attestation_state":"computed","paper":{"title":"On the Cycle Structure of Mallows Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alexey Gladkich, Ron Peled","submitted_at":"2016-01-26T12:24:32Z","abstract_excerpt":"We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\\pi \\in \\mathbb{S}_n$ is proportional to $q^{\\textrm{inv}(\\pi)}$ where $0<q\\le 1$ and $\\textrm{inv}(\\pi)$ is the number of inversions in $\\pi$.\n  We show that the expected length of the cycle containing a given point is of order $\\min\\{(1-q)^{-2}, n\\}$. This marks the existence of two asymptotic regimes: with high probability, when $n$ tends to infinity with $(1-q)^{-2} \\ll n$ then all cycles have size $o(n)$ whereas when $n$ tends to infinity wit"},"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":"1601.06991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-26T12:24:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8d03356a5bbe622e8f60f4c35a4408aa8da4448397cbaeab849ecf86d82562e7","abstract_canon_sha256":"b770e0052f731ae083fd81557d3040d83e5d85443294247f0e3c967345448a96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:44.382450Z","signature_b64":"SUPwEqKJgrjFMr2eIbHGu3aivEi3rKcabR8jwBJPbCQyPF3EESZ6knVMikc2Tx6/KXBmRqIDCE8C9w8ifzlXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b00d98125e7f2f730f678b06955d43bcdeab8d7c3a23719a2db283a06e06a87e","last_reissued_at":"2026-05-18T00:35:44.381944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:44.381944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Cycle Structure of Mallows Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alexey Gladkich, Ron Peled","submitted_at":"2016-01-26T12:24:32Z","abstract_excerpt":"We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\\pi \\in \\mathbb{S}_n$ is proportional to $q^{\\textrm{inv}(\\pi)}$ where $0<q\\le 1$ and $\\textrm{inv}(\\pi)$ is the number of inversions in $\\pi$.\n  We show that the expected length of the cycle containing a given point is of order $\\min\\{(1-q)^{-2}, n\\}$. This marks the existence of two asymptotic regimes: with high probability, when $n$ tends to infinity with $(1-q)^{-2} \\ll n$ then all cycles have size $o(n)$ whereas when $n$ tends to infinity wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06991","kind":"arxiv","version":2},"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":"1601.06991","created_at":"2026-05-18T00:35:44.382007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.06991v2","created_at":"2026-05-18T00:35:44.382007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06991","created_at":"2026-05-18T00:35:44.382007+00:00"},{"alias_kind":"pith_short_12","alias_value":"WAGZQES6P4XX","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WAGZQES6P4XXGD3H","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WAGZQES6","created_at":"2026-05-18T12:30:48.956258+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/WAGZQES6P4XXGD3HRMDJKXKDXT","json":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT.json","graph_json":"https://pith.science/api/pith-number/WAGZQES6P4XXGD3HRMDJKXKDXT/graph.json","events_json":"https://pith.science/api/pith-number/WAGZQES6P4XXGD3HRMDJKXKDXT/events.json","paper":"https://pith.science/paper/WAGZQES6"},"agent_actions":{"view_html":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT","download_json":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT.json","view_paper":"https://pith.science/paper/WAGZQES6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.06991&json=true","fetch_graph":"https://pith.science/api/pith-number/WAGZQES6P4XXGD3HRMDJKXKDXT/graph.json","fetch_events":"https://pith.science/api/pith-number/WAGZQES6P4XXGD3HRMDJKXKDXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT/action/storage_attestation","attest_author":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT/action/author_attestation","sign_citation":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT/action/citation_signature","submit_replication":"https://pith.science/pith/WAGZQES6P4XXGD3HRMDJKXKDXT/action/replication_record"}},"created_at":"2026-05-18T00:35:44.382007+00:00","updated_at":"2026-05-18T00:35:44.382007+00:00"}