{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VULLE2XPX2CRDMCYE6J7L2GOEZ","short_pith_number":"pith:VULLE2XP","schema_version":"1.0","canonical_sha256":"ad16b26aefbe8511b0582793f5e8ce266e4b8d6eefefe7e9cbc3baddc0ff8fb9","source":{"kind":"arxiv","id":"1906.06036","version":1},"attestation_state":"computed","paper":{"title":"Linear extension numbers of $n$-element posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Noah Kravitz","submitted_at":"2019-06-14T06:07:10Z","abstract_excerpt":"We address the following natural but hitherto unstudied question: what are the possible linear extension numbers of an $n$-element poset? Let $\\mathbf{LE}(n)$ denote the set of all positive integers that arise as the number of linear extensions of some $n$-element poset. We show that $\\mathbf{LE}(n)$ skews towards the \"small\" end of the interval $[1,n!]$. More specifically, $\\mathbf{LE}(n)$ contains all of the positive integers up to $\\exp\\left(c\\frac{n}{\\log n}\\right)$ for some absolute constant $c$, and $|\\mathbf{LE}(n) \\cap ((n-1)!,n!]|<(n-3)!$. The proof of the former statement involves so"},"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":"1906.06036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-14T06:07:10Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bd0f83f267c8e04b2d8eb38a5c40403022c762e191c3feb0919b4e737ca14c17","abstract_canon_sha256":"e55433a3eb182b770a1dd559516809833d7ae98f2dcff6cbcaeecff90eec9d84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:19.970606Z","signature_b64":"2vq2pEeTp/kLrCmEKfI6y/q98JYn7jdwiqgAt/Os+n//gw83EYy+iQ+kA95BS0OjzzDJBilFHIjqpWIvt8paAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad16b26aefbe8511b0582793f5e8ce266e4b8d6eefefe7e9cbc3baddc0ff8fb9","last_reissued_at":"2026-05-17T23:43:19.969941Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:19.969941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear extension numbers of $n$-element posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Noah Kravitz","submitted_at":"2019-06-14T06:07:10Z","abstract_excerpt":"We address the following natural but hitherto unstudied question: what are the possible linear extension numbers of an $n$-element poset? Let $\\mathbf{LE}(n)$ denote the set of all positive integers that arise as the number of linear extensions of some $n$-element poset. We show that $\\mathbf{LE}(n)$ skews towards the \"small\" end of the interval $[1,n!]$. More specifically, $\\mathbf{LE}(n)$ contains all of the positive integers up to $\\exp\\left(c\\frac{n}{\\log n}\\right)$ for some absolute constant $c$, and $|\\mathbf{LE}(n) \\cap ((n-1)!,n!]|<(n-3)!$. The proof of the former statement involves so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06036","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":"1906.06036","created_at":"2026-05-17T23:43:19.970036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.06036v1","created_at":"2026-05-17T23:43:19.970036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06036","created_at":"2026-05-17T23:43:19.970036+00:00"},{"alias_kind":"pith_short_12","alias_value":"VULLE2XPX2CR","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VULLE2XPX2CRDMCY","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VULLE2XP","created_at":"2026-05-18T12:33:30.264802+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/VULLE2XPX2CRDMCYE6J7L2GOEZ","json":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ.json","graph_json":"https://pith.science/api/pith-number/VULLE2XPX2CRDMCYE6J7L2GOEZ/graph.json","events_json":"https://pith.science/api/pith-number/VULLE2XPX2CRDMCYE6J7L2GOEZ/events.json","paper":"https://pith.science/paper/VULLE2XP"},"agent_actions":{"view_html":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ","download_json":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ.json","view_paper":"https://pith.science/paper/VULLE2XP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.06036&json=true","fetch_graph":"https://pith.science/api/pith-number/VULLE2XPX2CRDMCYE6J7L2GOEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/VULLE2XPX2CRDMCYE6J7L2GOEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ/action/storage_attestation","attest_author":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ/action/author_attestation","sign_citation":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ/action/citation_signature","submit_replication":"https://pith.science/pith/VULLE2XPX2CRDMCYE6J7L2GOEZ/action/replication_record"}},"created_at":"2026-05-17T23:43:19.970036+00:00","updated_at":"2026-05-17T23:43:19.970036+00:00"}