{"paper":{"title":"Lower bounds for the Tur\\'an densities of daisies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Ellis, Dylan King","submitted_at":"2022-04-19T14:59:37Z","abstract_excerpt":"For integers $r \\geq 3$ and $t \\geq 2$, an $r$-uniform $t$-daisy $\\mathcal{D}^t_r$ is a family of $\\binom{2t}{t}$ $r$-element sets of the form $$\\{S \\cup T \\ : T\\subset U, \\ |T|=t \\}$$ for some sets $S,U$ with $|S|=r-t$, $|U|=2t$ and $S \\cap U = \\emptyset$. It was conjectured by Bollob\\'as, Leader and Malvenuto (and independently Bukh) that the Tur\\'an densities of $t$-daisies satisfy $\\lim\\limits_{r \\to \\infty} \\pi(\\mathcal{D}_r^t) = 0$ for all $t \\geq 2$; this has become a well-known problem, and it is still open for all values of $t$. In this paper, we give lower bounds for the Tur\\'an dens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.08930","kind":"arxiv","version":5},"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/2204.08930/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"}