{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:C3CG7XMEXVWMRZYP6O5QM3EQAL","short_pith_number":"pith:C3CG7XME","schema_version":"1.0","canonical_sha256":"16c46fdd84bd6cc8e70ff3bb066c9002fb83d50c829a8f139939cded820a76ff","source":{"kind":"arxiv","id":"1303.3652","version":2},"attestation_state":"computed","paper":{"title":"Structure and enumeration of (3+1)-free posets","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":"2013-03-15T01:10:05Z","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 play a central role in the (3+1)-free conjecture of Stanley and Stembridge. Lewis and Zhang have enumerated (3+1)-free posets in the graded case by decomposing them into bipartite graphs, but until now the general enumeration problem has remained open. We give a finer decomposition into bipartite graphs which applies to all (3+1)-free posets and obtain generating functions which count (3+1)-free posets with labelled or unlabelled vertices. Using this decomposition, w"},"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":"1303.3652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-15T01:10:05Z","cross_cats_sorted":[],"title_canon_sha256":"a508e661233b4579a52fe405570a58e05a1cd3e6dda94a72ebf30d4b27c81a6a","abstract_canon_sha256":"9078dff055a8659b1824a7394156dba7c113017966d9099e6e730b56ceb3ca27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:39.188719Z","signature_b64":"oq9z1XHkkaD7shjob7gQ4CDewgD6B2IvnS0kWVHEKNpwtZNAf9gyn5D7ZOsqNRXYriXHKrQV+70D1lOWGd3tCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16c46fdd84bd6cc8e70ff3bb066c9002fb83d50c829a8f139939cded820a76ff","last_reissued_at":"2026-05-18T01:23:39.188075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:39.188075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure and enumeration of (3+1)-free posets","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":"2013-03-15T01:10:05Z","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 play a central role in the (3+1)-free conjecture of Stanley and Stembridge. Lewis and Zhang have enumerated (3+1)-free posets in the graded case by decomposing them into bipartite graphs, but until now the general enumeration problem has remained open. We give a finer decomposition into bipartite graphs which applies to all (3+1)-free posets and obtain generating functions which count (3+1)-free posets with labelled or unlabelled vertices. Using this decomposition, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3652","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":"1303.3652","created_at":"2026-05-18T01:23:39.188174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3652v2","created_at":"2026-05-18T01:23:39.188174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3652","created_at":"2026-05-18T01:23:39.188174+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3CG7XMEXVWM","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3CG7XMEXVWMRZYP","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3CG7XME","created_at":"2026-05-18T12:27:40.988391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.20019","citing_title":"How to Use Deep Learning to Identify Sufficient Conditions: A Case Study on Stanley's $e$-Positivity","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL","json":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL.json","graph_json":"https://pith.science/api/pith-number/C3CG7XMEXVWMRZYP6O5QM3EQAL/graph.json","events_json":"https://pith.science/api/pith-number/C3CG7XMEXVWMRZYP6O5QM3EQAL/events.json","paper":"https://pith.science/paper/C3CG7XME"},"agent_actions":{"view_html":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL","download_json":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL.json","view_paper":"https://pith.science/paper/C3CG7XME","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3652&json=true","fetch_graph":"https://pith.science/api/pith-number/C3CG7XMEXVWMRZYP6O5QM3EQAL/graph.json","fetch_events":"https://pith.science/api/pith-number/C3CG7XMEXVWMRZYP6O5QM3EQAL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL/action/storage_attestation","attest_author":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL/action/author_attestation","sign_citation":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL/action/citation_signature","submit_replication":"https://pith.science/pith/C3CG7XMEXVWMRZYP6O5QM3EQAL/action/replication_record"}},"created_at":"2026-05-18T01:23:39.188174+00:00","updated_at":"2026-05-18T01:23:39.188174+00:00"}