{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LDK5QFJIWHRN3U2AVCTZBL2KY7","short_pith_number":"pith:LDK5QFJI","schema_version":"1.0","canonical_sha256":"58d5d81528b1e2ddd340a8a790af4ac7e100c9f1f57918a9e5e9498422f7aadb","source":{"kind":"arxiv","id":"1809.01384","version":2},"attestation_state":"computed","paper":{"title":"Counting Consecutive Pattern Matches in $\\mathcal{S}_n(132)$ and $\\mathcal{S}_n(123)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dun Qiu, Jeffrey Remmel, Ran Pan","submitted_at":"2018-09-05T08:34:54Z","abstract_excerpt":"In this paper, we study the distribution of consecutive patterns in the set of 123-avoiding permutations and the set of 132-avoiding permutations, that is, in $\\mathcal{S}_n(123)$ and $\\mathcal{S}_n(132)$. We first study the distribution of consecutive pattern $\\gamma$-matches in $\\mathcal{S}_n(123)$ and $\\mathcal{S}_n(132)$ for each length 3 consecutive pattern $\\gamma$. Then we extend our methods to study the joint distributions of multiple consecutive patterns. Some more general cases are discussed in this paper as well."},"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":"1809.01384","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-05T08:34:54Z","cross_cats_sorted":[],"title_canon_sha256":"83d7629ba2e4c25b2c857a0ad62ed3fe17d2affeb1e719cab68e9c91344f4a9f","abstract_canon_sha256":"63ddb3388831761f4dffe2ffacdeda4235775de91a90c1ba573354994c40b1bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:58.325846Z","signature_b64":"2p9YUkePlxwDom48+oqV50uz1GAyKPilCfPt7KTs1uSuG4m0Gz7FSZV7HlAElNYt5Iy4tRaU7FImypB7qZ4WAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d5d81528b1e2ddd340a8a790af4ac7e100c9f1f57918a9e5e9498422f7aadb","last_reissued_at":"2026-05-17T23:56:58.325268Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:58.325268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Consecutive Pattern Matches in $\\mathcal{S}_n(132)$ and $\\mathcal{S}_n(123)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dun Qiu, Jeffrey Remmel, Ran Pan","submitted_at":"2018-09-05T08:34:54Z","abstract_excerpt":"In this paper, we study the distribution of consecutive patterns in the set of 123-avoiding permutations and the set of 132-avoiding permutations, that is, in $\\mathcal{S}_n(123)$ and $\\mathcal{S}_n(132)$. We first study the distribution of consecutive pattern $\\gamma$-matches in $\\mathcal{S}_n(123)$ and $\\mathcal{S}_n(132)$ for each length 3 consecutive pattern $\\gamma$. Then we extend our methods to study the joint distributions of multiple consecutive patterns. Some more general cases are discussed in this paper as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01384","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":"1809.01384","created_at":"2026-05-17T23:56:58.325357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01384v2","created_at":"2026-05-17T23:56:58.325357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01384","created_at":"2026-05-17T23:56:58.325357+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDK5QFJIWHRN","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDK5QFJIWHRN3U2A","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDK5QFJI","created_at":"2026-05-18T12:32:37.024351+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/LDK5QFJIWHRN3U2AVCTZBL2KY7","json":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7.json","graph_json":"https://pith.science/api/pith-number/LDK5QFJIWHRN3U2AVCTZBL2KY7/graph.json","events_json":"https://pith.science/api/pith-number/LDK5QFJIWHRN3U2AVCTZBL2KY7/events.json","paper":"https://pith.science/paper/LDK5QFJI"},"agent_actions":{"view_html":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7","download_json":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7.json","view_paper":"https://pith.science/paper/LDK5QFJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01384&json=true","fetch_graph":"https://pith.science/api/pith-number/LDK5QFJIWHRN3U2AVCTZBL2KY7/graph.json","fetch_events":"https://pith.science/api/pith-number/LDK5QFJIWHRN3U2AVCTZBL2KY7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7/action/storage_attestation","attest_author":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7/action/author_attestation","sign_citation":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7/action/citation_signature","submit_replication":"https://pith.science/pith/LDK5QFJIWHRN3U2AVCTZBL2KY7/action/replication_record"}},"created_at":"2026-05-17T23:56:58.325357+00:00","updated_at":"2026-05-17T23:56:58.325357+00:00"}