{"schema":"vela.problem-packet.v0.1","problem":1044,"statement":"Let $f(z)=\\prod_{i=1}^n(z-z_i)\\in\\mathbb{C}[x]$ where $\\lvert z_i\\rvert\\leq 1$ for all $i$. If $\\Lambda(f)$ is the maximum of the lengths of the boundaries of the connected components of\\[\\{ z: \\lvert f(z)\\rvert<1\\}\\]then determine the infimum of $\\Lambda(f)$.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}