{"schema":"vela.problem-packet.v0.1","problem":588,"statement":"Let $f_k(n)$ be minimal such that if $n$ points in $\\mathbb{R}^2$ have no $k+1$ points on a line then there must be at most $f_k(n)$ many lines containing at least $k$ points. Is it true that\\[f_k(n)=o(n^2)\\]for $k\\geq 4$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A006065","name":"Maximal number of 4-tree rows in n-tree orchard problem.","terms":"0,0,0,1,1,1,2,2,3,5,6,7,9,10,12,15,16,18,20,23","url":"https://oeis.org/A006065"},{"id":"A008997","name":"Orchard problem with 5 trees in a row (may not have all been proved optimal).","terms":"0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,7,9,10,11","url":"https://oeis.org/A008997"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}