{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2JIC6PTEPLZXM7O2TQCJLHXVNZ","short_pith_number":"pith:2JIC6PTE","schema_version":"1.0","canonical_sha256":"d2502f3e647af3767dda9c04959ef56e7a0b112092478e7f8623fc9b8a46238c","source":{"kind":"arxiv","id":"1102.5568","version":1},"attestation_state":"computed","paper":{"title":"Counting (3+1) - Avoiding permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce E. Sagan, M. D. Atkinson, Vincent Vatter","submitted_at":"2011-02-28T01:41:42Z","abstract_excerpt":"A poset is {\\it $(\\3+\\1)$-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the $(\\3+\\1)$-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\\pi$ where $i\\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\\pi$. So we say that a permutation $\\pi$ is {\\it $(\\3+\\1)$-free} or {\\it $(\\3+\\1)$-avoiding} if"},"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":"1102.5568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-28T01:41:42Z","cross_cats_sorted":[],"title_canon_sha256":"18d9c1e355c9ce449f875c0cbaf9256998c99fedc88d9596071e513baa19f9a9","abstract_canon_sha256":"44d7643ef24a00097f2ca3f08681a23936161bca3f15b9e1d2a0be84e65ffe8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:46.557267Z","signature_b64":"6mWiMENHfRxPLihR8UZ4Z9wunvpCchDFQzjg2FhFVk7AVgtCJ8/jozqzp08yWgUFo3LFDNgn+okBdBHL0yMLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2502f3e647af3767dda9c04959ef56e7a0b112092478e7f8623fc9b8a46238c","last_reissued_at":"2026-05-18T04:27:46.556818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:46.556818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting (3+1) - Avoiding permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce E. Sagan, M. D. Atkinson, Vincent Vatter","submitted_at":"2011-02-28T01:41:42Z","abstract_excerpt":"A poset is {\\it $(\\3+\\1)$-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the $(\\3+\\1)$-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\\pi$ where $i\\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\\pi$. So we say that a permutation $\\pi$ is {\\it $(\\3+\\1)$-free} or {\\it $(\\3+\\1)$-avoiding} if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5568","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":"1102.5568","created_at":"2026-05-18T04:27:46.556880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.5568v1","created_at":"2026-05-18T04:27:46.556880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5568","created_at":"2026-05-18T04:27:46.556880+00:00"},{"alias_kind":"pith_short_12","alias_value":"2JIC6PTEPLZX","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2JIC6PTEPLZXM7O2","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2JIC6PTE","created_at":"2026-05-18T12:26:18.847500+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/2JIC6PTEPLZXM7O2TQCJLHXVNZ","json":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ.json","graph_json":"https://pith.science/api/pith-number/2JIC6PTEPLZXM7O2TQCJLHXVNZ/graph.json","events_json":"https://pith.science/api/pith-number/2JIC6PTEPLZXM7O2TQCJLHXVNZ/events.json","paper":"https://pith.science/paper/2JIC6PTE"},"agent_actions":{"view_html":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ","download_json":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ.json","view_paper":"https://pith.science/paper/2JIC6PTE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.5568&json=true","fetch_graph":"https://pith.science/api/pith-number/2JIC6PTEPLZXM7O2TQCJLHXVNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2JIC6PTEPLZXM7O2TQCJLHXVNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ/action/storage_attestation","attest_author":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ/action/author_attestation","sign_citation":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ/action/citation_signature","submit_replication":"https://pith.science/pith/2JIC6PTEPLZXM7O2TQCJLHXVNZ/action/replication_record"}},"created_at":"2026-05-18T04:27:46.556880+00:00","updated_at":"2026-05-18T04:27:46.556880+00:00"}