AI 中文总结
该研究针对禁配置的Anstee-Sali猜想构造了一个由GPT-5.6 Sol发现的反例，证明其渐近结果与猜想预测不符，修正了相关理论结论。
AI 中文摘要
本注记提出了关于禁配置的Anstee-Sali猜想的一个反例。基本候选是6个顶点上的4-均匀族F₂={xyab,xybc,xycd,xyda}：一个固定的两顶点核心{x,y}连接到一个4-环的四条边。我们给出一个明确的认证，即每个因子为I、I^c或T的四重积都包含F₂，而I³则避免它。因此，X(F₂)=4，故猜想预测forb(m,F₂)=Θ(m³)。另一方面，从所有4-子集出发的标准随机调整论证给出forb(m,F₂)=Ω(m^(10/3))，其渐近大于m³。该例子由GPT-5.6 Sol发现。
英文摘要
This note propose a counterexample to the Anstee--Sali conjecture for forbidden configurations. The basic candidate is the $4$-uniform family \[ F_2=\{xyab,xybc,xycd,xyda\} \] on six vertices: a fixed two-vertex core $\{x,y\}$ joined to the four edges of a $4$-cycle. We give an explicit certificate that every four-fold product whose factors are of type $I$, $I^c$, or $T$ contains $F_2$, while $I^3$ avoids it. Thus, $X(F_2)=4$, so the conjecture predicts $\operatorname{forb}(m,F_2)=Θ(m^3)$. On the other hand, a result of Mubayi on complete multipartite hypergraphs implies \[ \operatorname{forb}(m,F_2)=Ω(m^{7/2}), \] which is asymptotically larger than $m^3$. The example was found by GPT-5.6 Sol.
Comments5 pages, updated a new bound based on Mubayi's result
