{"paper":{"title":"Ramsey-Tur\\'{a}n theory for partially-ordered sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gyula O.H. Katona, Yaping Mao","submitted_at":"2026-05-29T17:01:16Z","abstract_excerpt":"We introduce weak and strong poset Ramsey-Tur\\'an numbers for $t$-chains in host poset families, focusing on the Boolean lattice family $\\mathcal{B}=\\{B_n:n\\ge 1\\}$. For any poset $P$, we show $\\operatorname{RT}(\\mathcal{B};n,P,l,t)\\le \\operatorname{RT}^{\\sharp}(\\mathcal{B};n,P,l,t)$, with equality when $P$ is a chain. In particular, for $t=1$, $\\operatorname{RT}(\\mathcal{B};n,C_k,l)=\\operatorname{RT}^{\\sharp}(\\mathcal{B};n,C_k,l)=(k-1)(l-1)$. We also give universal upper bounds for both versions. For fixed $k,l,t$ with $\\min\\{l-1,k-1\\}\\ge 1$, we prove $\\operatorname{RT}^{\\sharp}(\\mathcal{B};n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31546","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.31546/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}