{"schema":"vela.problem-packet.v0.1","problem":20,"statement":"Let $f(n,k)$ be minimal such that every family $\\mathcal{F}$ of $n$-uniform sets with $\\lvert \\mathcal{F}\\rvert \\geq f(n,k)$ contains a $k$-sunflower. Is it true that\\[f(n,k) < c_k^n\\]for some constant $c_k>0$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A332077","name":"Square array of sunflower numbers Sun(m,n) = minimal number of distinct sets of cardinality <= m such that there is a sunflower with at least n sets among them, read by falling antidiagonals; m, n >= ","terms":"1,2,1,3,2,1,4,7,2,1,5,11,21,2,1,6,21","url":"https://oeis.org/A332077"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}