{"paper":{"title":"Generalized forbidden subposet problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Balazs Keszegh, Balazs Patkos, Daniel Gerbner","submitted_at":"2017-01-18T12:21:07Z","abstract_excerpt":"A subfamily $\\{F_1,F_2,\\dots,F_{|P|}\\}\\subseteq {\\cal F}$ of sets is a copy of a poset $P$ in ${\\cal F}$ if there exists a bijection $\\phi:P\\rightarrow \\{F_1,F_2,\\dots,F_{|P|}\\}$ such that whenever $x \\le_P x'$ holds, then so does $\\phi(x)\\subseteq \\phi(x')$. For a family ${\\cal F}$ of sets, let $c(P,{\\cal F})$ denote the number of copies of $P$ in ${\\cal F}$, and we say that ${\\cal F}$ is $P$-free if $c(P,{\\cal F})=0$ holds. For any two posets $P,Q$ let us denote by $La(n,P,Q)$ the maximum number of copies of $Q$ over all $P$-free families ${\\cal F} \\subseteq 2^{[n]}$, i.e. $\\max\\{c(Q,{\\cal F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05030","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"}