{"schema":"vela.problem-packet.v0.1","problem":499,"statement":"Let $M=(a_{ij})$ be a real $n\\times n$ doubly stochastic matrix (i.e. the entries are non-negative and each column and row sums to $1$). Does there exist some $\\sigma\\in S_n$ such that\\[\\prod_{1\\leq i\\leq n}a_{i\\sigma(i)}\\geq n^{-n}?\\]","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)"}