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We say that a family $\\mathcal{F}$ of subsets of $[n]=\\{1,2,...,n\\}$ contains a \\emph{rank-preserving} copy of $P$ if it contains a copy of $P$ such that elements of $P$ having the same rank are mapped to sets of same size in $\\mathcal{F}$. The largest size of a family of subsets of $[n]=\\{1,2,...,n\\}$ without containing a rank-preserving copy of $P$ as a subposet is denoted by $La_{rp}(n,P)$. Clearly, $La(n,P) \\le"},"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":"1710.09086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-25T06:49:27Z","cross_cats_sorted":[],"title_canon_sha256":"8266b97c00f9a40bcdbf3b165ff7c609213c3d2db9e5008073f5b5e4f63b0ea7","abstract_canon_sha256":"3354a1aefd3536db7f13e60abbf8777ab98cde6c55ebda1856a8354ca25f7b94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:00.402377Z","signature_b64":"htmDHyG/T0Gs1aKrNaB1zPjt+rjubShOUhCclyHNpzsQbqwtpLxq/jQhZcWcoyQcwgZBRyElwGAvxAtgkRvXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdda1d48e33141d828ac7a3e8499b2a759e5c1e78fe747091fc1dcafbb4f3f63","last_reissued_at":"2026-05-18T00:32:00.401777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:00.401777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forbidding rank-preserving copies of a poset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Bal\\'azs Patk\\'os, D\\'aniel Gerbner, D\\'aniel T. Nagy, M\\'at\\'e Vizer","submitted_at":"2017-10-25T06:49:27Z","abstract_excerpt":"The maximum size, $La(n,P)$, of a family of subsets of $[n]=\\{1,2,...,n\\}$ without containing a copy of $P$ as a subposet, has been intensively studied.\n  Let $P$ be a graded poset. We say that a family $\\mathcal{F}$ of subsets of $[n]=\\{1,2,...,n\\}$ contains a \\emph{rank-preserving} copy of $P$ if it contains a copy of $P$ such that elements of $P$ having the same rank are mapped to sets of same size in $\\mathcal{F}$. The largest size of a family of subsets of $[n]=\\{1,2,...,n\\}$ without containing a rank-preserving copy of $P$ as a subposet is denoted by $La_{rp}(n,P)$. 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