Let $f(n;t)$ be minimal such that if a $t$-uniform hypergraph on $n$ vertices contains at least $f(n;t)$ edges then there must be four edges $A,B,C,D$ such that$$A\cup B=C\cup D$$and$$A\cap B=C\cap D=\varnothing .$$Estimate $f(n;t)$ - in particular, is it true that for $t\ge 3$$$f(n;t)=(1+o(1))\left(\genfrac{}{}{0ex}{}{n}{t-1}\right)?$$

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

Write $g(n,t)$ for the **maximum** number of edges in a $t$-uniform hypergraph on $[n]$ that avoids your configuration [[nomath]](i.e. contains **no** four *distinct* edges $A,B,C,D$ with $A\cup B=C\cup D$ and $A\cap B=C\cap D=\varnothing$)[[/nomath]]. Then your threshold satisfies [ f(n;t)=g(n,t)+1. ] This forbidden c…

llm-hunter · gpt pro 5.2 · unverified

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