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The poset $Y'_{k+1, 2}$ is the dual of $Y_{k+1, 2}$ Let $\\rm{La}^{\\sharp}(n,\\{Y_{k+1, 2}, Y'_{k+1, 2}\\})$ be the size of the largest family $\\mathcal{F} \\subset 2^{[n]}$ that contains neither $Y_{k+1,2}$ nor $Y'_{k+1,2}$ as an induced subposet. Methuku and Tompkins proved that $\\rm{La}^{\\sharp}(n, \\{Y_{3,2}, Y'_{3,2}\\}) = \\Sigma(n,2)$ for $n \\ge 3$ and they conjectured the generalization that if $k \\ge 2$ is an integer and $n \\ge k+1$"},"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":"1710.05057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-13T19:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"282d6b1db0b4badfc1a686ab1a9375e517174bcca11b65c4b0a6edc7595dd635","abstract_canon_sha256":"e323e7250d3300410caff441709413e6c67ba8f44842cfe591a6e738544c6435"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:52.097434Z","signature_b64":"qDESjTJuUG+IIKbvvDlztFWHX4yyY6zrTCflHpK1TteYq66ohQCBhJcbHaJU3WmMVGtPygQijpvW4tGKl2FmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce3903294dac38c93131b12ea4f0a9e511243b0261086b97bac29681b67c62db","last_reissued_at":"2026-05-18T00:27:52.096818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:52.096818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simple discharging method for forbidden subposet problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Andrew Uzzell, Ryan R. Martin, Shanise Walker","submitted_at":"2017-10-13T19:27:02Z","abstract_excerpt":"The poset $Y_{k+1, 2}$ consists of $k+2$ distinct elements $x_1$, $x_2$, \\dots, $x_{k}$, $y_1$,$y_2$, such that $x_1 \\le x_2 \\le \\dots \\le x_{k} \\le y_1$,~$y_2$. The poset $Y'_{k+1, 2}$ is the dual of $Y_{k+1, 2}$ Let $\\rm{La}^{\\sharp}(n,\\{Y_{k+1, 2}, Y'_{k+1, 2}\\})$ be the size of the largest family $\\mathcal{F} \\subset 2^{[n]}$ that contains neither $Y_{k+1,2}$ nor $Y'_{k+1,2}$ as an induced subposet. Methuku and Tompkins proved that $\\rm{La}^{\\sharp}(n, \\{Y_{3,2}, Y'_{3,2}\\}) = \\Sigma(n,2)$ for $n \\ge 3$ and they conjectured the generalization that if $k \\ge 2$ is an integer and $n \\ge k+1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05057","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":"1710.05057","created_at":"2026-05-18T00:27:52.096912+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.05057v2","created_at":"2026-05-18T00:27:52.096912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05057","created_at":"2026-05-18T00:27:52.096912+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZY4QGKKNVQ4M","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZY4QGKKNVQ4MSMJR","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZY4QGKKN","created_at":"2026-05-18T12:31:59.375834+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/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U","json":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U.json","graph_json":"https://pith.science/api/pith-number/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/graph.json","events_json":"https://pith.science/api/pith-number/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/events.json","paper":"https://pith.science/paper/ZY4QGKKN"},"agent_actions":{"view_html":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U","download_json":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U.json","view_paper":"https://pith.science/paper/ZY4QGKKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.05057&json=true","fetch_graph":"https://pith.science/api/pith-number/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/graph.json","fetch_events":"https://pith.science/api/pith-number/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/action/storage_attestation","attest_author":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/action/author_attestation","sign_citation":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/action/citation_signature","submit_replication":"https://pith.science/pith/ZY4QGKKNVQ4MSMJRWEXKJ4FJ4U/action/replication_record"}},"created_at":"2026-05-18T00:27:52.096912+00:00","updated_at":"2026-05-18T00:27:52.096912+00:00"}