{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:44LQZ5ZXUG3G5SWVG332CB2Z3J","short_pith_number":"pith:44LQZ5ZX","schema_version":"1.0","canonical_sha256":"e7170cf737a1b66ecad536f7a10759da4e83a657312aa6d421f09f1ddf2df042","source":{"kind":"arxiv","id":"1212.5356","version":2},"attestation_state":"computed","paper":{"title":"Structure and enumeration of (3+1)-free posets (extended abstract)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro H. Morales, Eric Rowland, Mathieu Guay-Paquet","submitted_at":"2012-12-21T08:22:59Z","abstract_excerpt":"A poset is (3+1)-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets are the subject of the (3+1)-free conjecture of Stanley and Stembridge. Recently, Lewis and Zhang have enumerated \\emph{graded} (3+1)-free posets, but until now the general enumeration problem has remained open. We enumerate all (3+1)-free posets by giving a decomposition into bipartite graphs, and obtain generating functions for (3+1)-free posets with labelled or unlabelled vertices."},"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":"1212.5356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-21T08:22:59Z","cross_cats_sorted":[],"title_canon_sha256":"b34b28d38f4663ebb9dc8fd7acffd25ad25529389e5d769857114b5d33b70255","abstract_canon_sha256":"701608c17cf5aabf2f261d9606001460daa9a8b9fa806fe4a95a15bc4bb06977"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.301468Z","signature_b64":"AC7vP3UqUEN+dd6yu2qD4E8suqJmgoGs3nGTED+PakMKfTHRGFSdHvlTNbEK7LpTNdlsaIAY4P5yFgDZas1NCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7170cf737a1b66ecad536f7a10759da4e83a657312aa6d421f09f1ddf2df042","last_reissued_at":"2026-05-18T02:54:05.300906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.300906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure and enumeration of (3+1)-free posets (extended abstract)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro H. Morales, Eric Rowland, Mathieu Guay-Paquet","submitted_at":"2012-12-21T08:22:59Z","abstract_excerpt":"A poset is (3+1)-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets are the subject of the (3+1)-free conjecture of Stanley and Stembridge. Recently, Lewis and Zhang have enumerated \\emph{graded} (3+1)-free posets, but until now the general enumeration problem has remained open. We enumerate all (3+1)-free posets by giving a decomposition into bipartite graphs, and obtain generating functions for (3+1)-free posets with labelled or unlabelled vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5356","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":"1212.5356","created_at":"2026-05-18T02:54:05.300997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5356v2","created_at":"2026-05-18T02:54:05.300997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5356","created_at":"2026-05-18T02:54:05.300997+00:00"},{"alias_kind":"pith_short_12","alias_value":"44LQZ5ZXUG3G","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"44LQZ5ZXUG3G5SWV","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"44LQZ5ZX","created_at":"2026-05-18T12:26:53.410803+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/44LQZ5ZXUG3G5SWVG332CB2Z3J","json":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J.json","graph_json":"https://pith.science/api/pith-number/44LQZ5ZXUG3G5SWVG332CB2Z3J/graph.json","events_json":"https://pith.science/api/pith-number/44LQZ5ZXUG3G5SWVG332CB2Z3J/events.json","paper":"https://pith.science/paper/44LQZ5ZX"},"agent_actions":{"view_html":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J","download_json":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J.json","view_paper":"https://pith.science/paper/44LQZ5ZX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5356&json=true","fetch_graph":"https://pith.science/api/pith-number/44LQZ5ZXUG3G5SWVG332CB2Z3J/graph.json","fetch_events":"https://pith.science/api/pith-number/44LQZ5ZXUG3G5SWVG332CB2Z3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J/action/storage_attestation","attest_author":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J/action/author_attestation","sign_citation":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J/action/citation_signature","submit_replication":"https://pith.science/pith/44LQZ5ZXUG3G5SWVG332CB2Z3J/action/replication_record"}},"created_at":"2026-05-18T02:54:05.300997+00:00","updated_at":"2026-05-18T02:54:05.300997+00:00"}