{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QF5LJME66GXFNOLYCS4WWFKLZH","short_pith_number":"pith:QF5LJME6","schema_version":"1.0","canonical_sha256":"817ab4b09ef1ae56b97814b96b154bc9d125fb9bfb8f73381284663163fb1aee","source":{"kind":"arxiv","id":"1902.08809","version":2},"attestation_state":"computed","paper":{"title":"Faster and simpler algorithms for finding large patterns in permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"L\\'aszl\\'o Kozma","submitted_at":"2019-02-23T16:24:20Z","abstract_excerpt":"Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length $n$ contains a given pattern of length $k$.\n  In this work we give two new algorithms for this well-studied problem, one whose running time is $n^{0.44k+o(k)}$, and one whose running time is the better of $O(1.6181^n)$ and $n^{k/2+o(k)}$. These results improve the earlier best bounds of Ahal and Rabinovi"},"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":"1902.08809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-23T16:24:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"2182b617de4a6ed2f51edcb3cf3419cb691295d190489087f7aa62a3dc021956","abstract_canon_sha256":"d6c27b4a4d3fa1bc48c11eeddd1a8e68682ba84c758600d8ecce90a57501cc7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:30.351605Z","signature_b64":"cLzj+Cp83gVjCpb0/uDb9kLNmfgLCIZnPAMsjeL0UfOSMdhTQ3Lk54rMhhlKVcPK7GkTSTsLvJDD4ICATLocAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"817ab4b09ef1ae56b97814b96b154bc9d125fb9bfb8f73381284663163fb1aee","last_reissued_at":"2026-05-17T23:48:30.350911Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:30.350911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faster and simpler algorithms for finding large patterns in permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"L\\'aszl\\'o Kozma","submitted_at":"2019-02-23T16:24:20Z","abstract_excerpt":"Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length $n$ contains a given pattern of length $k$.\n  In this work we give two new algorithms for this well-studied problem, one whose running time is $n^{0.44k+o(k)}$, and one whose running time is the better of $O(1.6181^n)$ and $n^{k/2+o(k)}$. These results improve the earlier best bounds of Ahal and Rabinovi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08809","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":"1902.08809","created_at":"2026-05-17T23:48:30.351027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.08809v2","created_at":"2026-05-17T23:48:30.351027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08809","created_at":"2026-05-17T23:48:30.351027+00:00"},{"alias_kind":"pith_short_12","alias_value":"QF5LJME66GXF","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"QF5LJME66GXFNOLY","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"QF5LJME6","created_at":"2026-05-18T12:33:27.125529+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/QF5LJME66GXFNOLYCS4WWFKLZH","json":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH.json","graph_json":"https://pith.science/api/pith-number/QF5LJME66GXFNOLYCS4WWFKLZH/graph.json","events_json":"https://pith.science/api/pith-number/QF5LJME66GXFNOLYCS4WWFKLZH/events.json","paper":"https://pith.science/paper/QF5LJME6"},"agent_actions":{"view_html":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH","download_json":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH.json","view_paper":"https://pith.science/paper/QF5LJME6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.08809&json=true","fetch_graph":"https://pith.science/api/pith-number/QF5LJME66GXFNOLYCS4WWFKLZH/graph.json","fetch_events":"https://pith.science/api/pith-number/QF5LJME66GXFNOLYCS4WWFKLZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH/action/storage_attestation","attest_author":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH/action/author_attestation","sign_citation":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH/action/citation_signature","submit_replication":"https://pith.science/pith/QF5LJME66GXFNOLYCS4WWFKLZH/action/replication_record"}},"created_at":"2026-05-17T23:48:30.351027+00:00","updated_at":"2026-05-17T23:48:30.351027+00:00"}