Let $r \geq 2$ and $A_{1}, \dots, A_{m} \subseteq {1, \dots, n}$ be such that $A_{i} \neq \subseteq A_{j}$ for all $i \neq = j$ and for any $t$ if there exists some $i$ with $∣ A_{i} ∣ = t$ then there must exist at least $r$ sets of that size.How large must $n$ be (as a function of $r$ ) to ensure that there is such a family which achieves $n - 3$ distinct sizes of sets?

Worked, still open.

combinatorics · open · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let me first restate the combinatorial object in a standard way:

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

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