{"schema":"vela.problem-packet.v0.1","problem":21,"statement":"Let $f(n)$ be minimal such that there is an intersecting family $\\mathcal{F}$ of sets of size $n$ (so $A\\cap B\\neq\\emptyset$ for all $A,B\\in \\mathcal{F}$) with $\\lvert \\mathcal{F}\\rvert=f(n)$ such that any set $S$ with $\\lvert S\\rvert \\leq n-1$ is disjoint from at least one $A\\in \\mathcal{F}$.Is it true that\\[f(n) \\ll n?\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A391599","name":"Minimum size of an intersecting family of n-sets such that every set of size at most n-1 is disjoint from at least one member of the family.","terms":"1,3,6,9,13","url":"https://oeis.org/A391599"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}