{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z2XMISPAUES4EZV7NDKD335DU4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"91eee4d32888156ebfa1d6b853f163c5c3b79793d389ab9395501ba505531561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-15T10:51:39Z","title_canon_sha256":"839a96f7c2b3f6cb52e1a09d21607e523afa619a2cdfd7eb330ce02b10ead6b2"},"schema_version":"1.0","source":{"id":"1611.04784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04784","created_at":"2026-05-18T00:58:49Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04784v1","created_at":"2026-05-18T00:58:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04784","created_at":"2026-05-18T00:58:49Z"},{"alias_kind":"pith_short_12","alias_value":"Z2XMISPAUES4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z2XMISPAUES4EZV7","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z2XMISPA","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:bbc2645aa4aa5c34eedb69b524b9e83da148c295641522fa0c7a68ff47eb5bf6","target":"graph","created_at":"2026-05-18T00:58:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The in-situ permutation algorithm due to MacLeod replaces $(x_{1},\\cdots,x_{n})$ by $(x_{p(1)},\\cdots,x_{p(n)})$ where $\\pi=(p(1),\\cdots,p(n))$ is a permutation of $\\{1,2,\\cdots,n\\}$ using at most $O(1)$ space. Kirshenhofer, Prodinger and Tichy have shown that the major cost incurred in the algorithm satisfies a recurrence similar to sequence of the number of key comparisons needed by the Quicksort algorithm to sort an array of $n$ randomly permuted items. Further, Hwang has proved that the normalized cost converges in distribution. Here, following Neininger and R\\\"uschendorf, we prove the tha","authors_text":"Sumit Kumar Jha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-15T10:51:39Z","title":"Rate of convergence of major cost incurred in the in-situ permutation algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04784","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c0e486eaadd30f2b6aefe2a0b3b24b864e88054550834f8ff9aed183de3b6ea6","target":"record","created_at":"2026-05-18T00:58:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"91eee4d32888156ebfa1d6b853f163c5c3b79793d389ab9395501ba505531561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-15T10:51:39Z","title_canon_sha256":"839a96f7c2b3f6cb52e1a09d21607e523afa619a2cdfd7eb330ce02b10ead6b2"},"schema_version":"1.0","source":{"id":"1611.04784","kind":"arxiv","version":1}},"canonical_sha256":"ceaec449e0a125c266bf68d43defa3a706267788cce2755c3acac7abd956d61a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceaec449e0a125c266bf68d43defa3a706267788cce2755c3acac7abd956d61a","first_computed_at":"2026-05-18T00:58:49.906879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:49.906879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tEsYqE1fG/KGkFmSE8j4wPejkSXz6MuAPFehVXiAQjw6PJFaBz7MrzBRPESyg61Ij7sUZWd+hNC87yl4UwGaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:49.907695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0e486eaadd30f2b6aefe2a0b3b24b864e88054550834f8ff9aed183de3b6ea6","sha256:bbc2645aa4aa5c34eedb69b524b9e83da148c295641522fa0c7a68ff47eb5bf6"],"state_sha256":"85d9bb1f27dca22e6dc62d0727d32bc0b64333bd5b1d42f3a181d609725b120d"}