{"schema":"vela.problem-packet.v0.1","problem":447,"statement":"How large can a union-free collection $\\mathcal{F}$ of subsets of $[n]$ be? By union-free we mean there are no solutions to $A\\cup B=C$ with distinct $A,B,C\\in \\mathcal{F}$. Must $\\lvert \\mathcal{F}\\rvert =o(2^n)$? Perhaps even\\[\\lvert \\mathcal{F}\\rvert <(1+o(1))\\binom{n}{\\lfloor n/2\\rfloor}?\\]","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)"}