论文标题
有限的超级图式家庭，具有丰富的极值Turán结构
Finite Hypergraph Families with Rich Extremal Turán Constructions via Mixing Patterns
论文作者
论文摘要
我们证明，对于任何有限的最小$ r $ graph图案，都有有限的家庭$ \ mathcal f $ forbidden $ r $ graphs，因此，$ \ mathcal f $ $ \ mathcal f $的极端turán构造是可以通过任何方式通过任何方式通过bliffers和recursion和recursion获得给定模式来获得的最大$ r $ graphs。这扩展了第二作者\ cite {pi14}的结果，其中为单个模式建立了上述语句。 我们提出了此结果的两个应用。首先，我们构建了一个有限的家庭$ \ Mathcal f $ $ 3 $ - 绘图，因此每个大订单$ n $的最大$ \ Mathcal f $ -3 $ 3 $ 3 $ graphs呈指数指数，此外，相应的Turán问题不是有限稳定的。其次，我们证明存在有限的家族$ \ MATHCAL {F} $ $ 3 $ - 绘图，其可行区域功能的最大值在一组正式Hausdorff尺寸上获得了最大值。
We prove that, for any finite set of minimal $r$-graph patterns, there is a finite family $\mathcal F$ of forbidden $r$-graphs such that the extremal Turán constructions for $\mathcal F$ are precisely the maximum $r$-graphs obtainable from mixing the given patterns in any way via blowups and recursion. This extends the result by the second author \cite{PI14}, where the above statement was established for a single pattern. We present two applications of this result. First, we construct a finite family $\mathcal F$ of $3$-graphs such that there are exponentially many maximum $\mathcal F$-free $3$-graphs of each large order $n$ and, moreover, the corresponding Turán problem is not finitely stable. Second, we show that there exists a finite family $\mathcal{F}$ of $3$-graphs whose feasible region function attains its maximum on a Cantor-type set of positive Hausdorff dimension.
