{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IOIVLBPBOAZZEK6ZOYIITLOEXF","short_pith_number":"pith:IOIVLBPB","schema_version":"1.0","canonical_sha256":"43915585e17033922bd9761089adc4b961229c3629713dd8a296587d77ea884f","source":{"kind":"arxiv","id":"1408.5783","version":2},"attestation_state":"computed","paper":{"title":"An improvement of the general bound on the largest family of subsets avoiding a subposet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2014-08-25T14:56:01Z","abstract_excerpt":"Let $La(n,P)$ be the maximum size of a family of subsets of $[n]= \\{1,2, ..., n \\}$ not containing $P$ as a (weak) subposet, and let $h(P)$ be the length of a longest chain in $P$. The best known upper bound for $La(n,P)$ in terms of $|P|$ and $h(P)$ is due to Chen and Li, who showed that $La(n,P) \\le \\frac{1}{m+1} \\left(|P| + \\frac{1}{2}(m^2 +3m-2)(h(P)-1) -1 \\right) {\\binom {n} {\\lfloor n/2 \\rfloor}}$ for any fixed $m \\ge 1$.\n  In this paper we show that $La(n,P) \\le \\frac{1}{2^{k-1}} (|P| + (3k-5)2^{k-2}(h(P)-1) - 1 ) {n \\choose {\\lfloor n/2\\rfloor} }$ for any fixed $k \\ge 2$, improving the"},"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":"1408.5783","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T14:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"d2099af480781bfe9733116264a21a8b0a9a6bd30e737f2bd4a9c6012452f5ff","abstract_canon_sha256":"877221bd603a318f425b92e873ed9b2c2573bed617a5825592f35b946c017da2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:18.564991Z","signature_b64":"OVL5vUNCX8LeMkwblVRTjrOzSPlKoP52MgKJC/2WAMrU9DAAfrfKm3ZD6HVldzQqa0DCPsAKlVrFd/S7ZHi7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43915585e17033922bd9761089adc4b961229c3629713dd8a296587d77ea884f","last_reissued_at":"2026-05-18T01:18:18.564299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:18.564299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An improvement of the general bound on the largest family of subsets avoiding a subposet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2014-08-25T14:56:01Z","abstract_excerpt":"Let $La(n,P)$ be the maximum size of a family of subsets of $[n]= \\{1,2, ..., n \\}$ not containing $P$ as a (weak) subposet, and let $h(P)$ be the length of a longest chain in $P$. The best known upper bound for $La(n,P)$ in terms of $|P|$ and $h(P)$ is due to Chen and Li, who showed that $La(n,P) \\le \\frac{1}{m+1} \\left(|P| + \\frac{1}{2}(m^2 +3m-2)(h(P)-1) -1 \\right) {\\binom {n} {\\lfloor n/2 \\rfloor}}$ for any fixed $m \\ge 1$.\n  In this paper we show that $La(n,P) \\le \\frac{1}{2^{k-1}} (|P| + (3k-5)2^{k-2}(h(P)-1) - 1 ) {n \\choose {\\lfloor n/2\\rfloor} }$ for any fixed $k \\ge 2$, improving the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5783","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":"1408.5783","created_at":"2026-05-18T01:18:18.564424+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5783v2","created_at":"2026-05-18T01:18:18.564424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5783","created_at":"2026-05-18T01:18:18.564424+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOIVLBPBOAZZ","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOIVLBPBOAZZEK6Z","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOIVLBPB","created_at":"2026-05-18T12:28:33.132498+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/IOIVLBPBOAZZEK6ZOYIITLOEXF","json":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF.json","graph_json":"https://pith.science/api/pith-number/IOIVLBPBOAZZEK6ZOYIITLOEXF/graph.json","events_json":"https://pith.science/api/pith-number/IOIVLBPBOAZZEK6ZOYIITLOEXF/events.json","paper":"https://pith.science/paper/IOIVLBPB"},"agent_actions":{"view_html":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF","download_json":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF.json","view_paper":"https://pith.science/paper/IOIVLBPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5783&json=true","fetch_graph":"https://pith.science/api/pith-number/IOIVLBPBOAZZEK6ZOYIITLOEXF/graph.json","fetch_events":"https://pith.science/api/pith-number/IOIVLBPBOAZZEK6ZOYIITLOEXF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF/action/storage_attestation","attest_author":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF/action/author_attestation","sign_citation":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF/action/citation_signature","submit_replication":"https://pith.science/pith/IOIVLBPBOAZZEK6ZOYIITLOEXF/action/replication_record"}},"created_at":"2026-05-18T01:18:18.564424+00:00","updated_at":"2026-05-18T01:18:18.564424+00:00"}