论文标题
部分可观测时空混沌系统的无模型预测
A note on distinct differences in $t$-intersecting families
论文作者
论文摘要
对于一个$ \ {1,2，\ ldots，n \} $的子集的$ \ Mathcal {f} $ $ \ mathcal {f} $。家庭$ \ Mathcal {f} $称为$ t $ - 更正家庭，如果用于某些正整数$ t $，而任意两个成员$ f，g \ in \ Mathcal {f} $我们有$ | f \ cap g | \ geq t $。如果$ t = 1 $，则家庭$ \ Mathcal {f} $简单地称为相交。最近，弗兰克尔（Frankl）证明了$ \ mathcal {d}（\ Mathcal {f}）$的上限，用于相交家庭$ \ Mathcal {f} $。在本说明中，我们将Frankl的结果扩展到了$ t $的建立家庭。
For a family $\mathcal{F}$ of subsets of $\{1,2,\ldots,n\}$, let $\mathcal{D}(\mathcal{F}) = \{F\setminus G: F, G \in \mathcal{F}\}$ be the collection of all (setwise) differences of $\mathcal{F}$. The family $\mathcal{F}$ is called a $t$-intersecting family, if for some positive integer $t$ and any two members $F, G \in \mathcal{F}$ we have $|F\cap G| \geq t$. The family $\mathcal{F}$ is simply called intersecting if $t=1$. Recently, Frankl proved an upper bound on the size of $\mathcal{D}(\mathcal{F})$ for the intersecting families $\mathcal{F}$. In this note we extend the result of Frankl to $t$-intersecting families.
