{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Z2Q4AXSVHA4HB7E3UJ6F4YFXFU","short_pith_number":"pith:Z2Q4AXSV","schema_version":"1.0","canonical_sha256":"cea1c05e55383870fc9ba27c5e60b72d379fbab876c991cc27533511e5b0de01","source":{"kind":"arxiv","id":"1906.07365","version":1},"attestation_state":"computed","paper":{"title":"Consecutive patterns in inversion sequences II: avoiding patterns of relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Juan S. Auli, Sergi Elizalde","submitted_at":"2019-06-18T03:55:37Z","abstract_excerpt":"Inversion sequences are integer sequences $e=e_{1}e_{2}\\dots e_{n}$ such that $0\\leq e_{i}<i$ for each $i$. The study of patterns in inversion sequences was initiated by Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck in the classical (non-consecutive) case, and later by Auli--Elizalde in the consecutive case, where the entries of a pattern are required to occur in adjacent positions. In this paper we continue this investigation by considering {\\em consecutive patterns of relations}, in analogy to the work of Martinez--Savage in the classical case. Specifically, given two binary re"},"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":"1906.07365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-18T03:55:37Z","cross_cats_sorted":[],"title_canon_sha256":"86b97497e58a6707d25ba661324df8af75bba3c0d1a2512d6c9f6bc62fcc1202","abstract_canon_sha256":"678aaddafbcee893dc0767d70160ee7894cba6d4c5228089d9f717514c94d70d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:08.089700Z","signature_b64":"icgQ3XSYLNswAzXHxP8Lb+92lxoWDLcee766HznJ9LTguILEgfK5mbfdsUu5A0d0yRsu0d2vtjFapcE5gHDODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea1c05e55383870fc9ba27c5e60b72d379fbab876c991cc27533511e5b0de01","last_reissued_at":"2026-05-17T23:43:08.089039Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:08.089039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consecutive patterns in inversion sequences II: avoiding patterns of relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Juan S. Auli, Sergi Elizalde","submitted_at":"2019-06-18T03:55:37Z","abstract_excerpt":"Inversion sequences are integer sequences $e=e_{1}e_{2}\\dots e_{n}$ such that $0\\leq e_{i}<i$ for each $i$. The study of patterns in inversion sequences was initiated by Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck in the classical (non-consecutive) case, and later by Auli--Elizalde in the consecutive case, where the entries of a pattern are required to occur in adjacent positions. In this paper we continue this investigation by considering {\\em consecutive patterns of relations}, in analogy to the work of Martinez--Savage in the classical case. Specifically, given two binary re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07365","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":"1906.07365","created_at":"2026-05-17T23:43:08.089146+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.07365v1","created_at":"2026-05-17T23:43:08.089146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07365","created_at":"2026-05-17T23:43:08.089146+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2Q4AXSVHA4H","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2Q4AXSVHA4HB7E3","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2Q4AXSV","created_at":"2026-05-18T12:33:33.725879+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/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU","json":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU.json","graph_json":"https://pith.science/api/pith-number/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/graph.json","events_json":"https://pith.science/api/pith-number/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/events.json","paper":"https://pith.science/paper/Z2Q4AXSV"},"agent_actions":{"view_html":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU","download_json":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU.json","view_paper":"https://pith.science/paper/Z2Q4AXSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.07365&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/action/storage_attestation","attest_author":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/action/author_attestation","sign_citation":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/action/citation_signature","submit_replication":"https://pith.science/pith/Z2Q4AXSVHA4HB7E3UJ6F4YFXFU/action/replication_record"}},"created_at":"2026-05-17T23:43:08.089146+00:00","updated_at":"2026-05-17T23:43:08.089146+00:00"}