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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","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T14:56:01Z","title":"An improvement of the general bound on the largest family of subsets avoiding a subposet"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5783","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4b2851182b138baffcd98057bd3ce731556a84a9fdd7daf3d536588acb21933f","target":"record","created_at":"2026-05-18T01:18:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"877221bd603a318f425b92e873ed9b2c2573bed617a5825592f35b946c017da2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T14:56:01Z","title_canon_sha256":"d2099af480781bfe9733116264a21a8b0a9a6bd30e737f2bd4a9c6012452f5ff"},"schema_version":"1.0","source":{"id":"1408.5783","kind":"arxiv","version":2}},"canonical_sha256":"43915585e17033922bd9761089adc4b961229c3629713dd8a296587d77ea884f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43915585e17033922bd9761089adc4b961229c3629713dd8a296587d77ea884f","first_computed_at":"2026-05-18T01:18:18.564299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:18.564299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OVL5vUNCX8LeMkwblVRTjrOzSPlKoP52MgKJC/2WAMrU9DAAfrfKm3ZD6HVldzQqa0DCPsAKlVrFd/S7ZHi7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:18.564991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5783","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b2851182b138baffcd98057bd3ce731556a84a9fdd7daf3d536588acb21933f","sha256:800ef88e67375bfa577effbfbfc3742f1d06d2d316ec63de8cdb3d92058e73b2"],"state_sha256":"6488060ece4738fe6db4d838e94d573bf821e2d05a7bf7b01fdf879a90097a07"}