{"schema":"vela.problem-packet.v0.1","problem":171,"statement":"Is it true that for every $\\epsilon>0$ and integer $t\\geq 1$, if $N$ is sufficiently large and $A$ is a subset of $[t]^N$ of size at least $\\epsilon t^N$ then $A$ must contain a combinatorial line $P$ (a set $P=\\{p_1,\\ldots,p_t\\}$ where for each coordinate $1\\leq j\\leq t$ the $j$th coordinate of $p_i$ is either $i$ or constant).","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A156989","name":"Largest size of a subset of {1,2,3}^n that does not contain any combinatorial lines (i.e., strings formed by 1, 2, 3, and at least one instance of a wildcard x, with x then substituted for 1, 2, or 3,","terms":"1,2,6,18,52,150,450","url":"https://oeis.org/A156989"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}