论文标题
三角形的T-t-t-Ctlectect家庭
Triangles in r-wise t-intersecting families
论文作者
论文摘要
令$ t $，$ r $，$ k $和$ n $为正整数和$ \ nathcal {f} $ $ k $ -subsets a $ n $ -set $ v $的家族。家庭$ \ cf $是$ r $ -iswise $ t $ -t $ - 如果对于任何$ f_1，\ ldots，f_r \ in \ cf $，我们有$ \ abs {\ cap_ {i = 1}^{r} f_i} f_i} f_i} \ gs t $。 $ r $ -wise $ t $ -t $ - iStecting家族的$ r + 1 $ sets $ \ {t_1，\ ldots，t_ {r + 1} \} $称为$（r + 1，t）$ -triangle，如果$ | \ ls t -1 $。在本文中，我们证明，如果$ n \ gs n_0（r，t，k）$，那么$ r $ - $ t $ t $ - iTTERTING $ \ cf \ cf \ subseteq \ binom {[n]} {n]} {k} {k} $ contance contance cully curly curly curly curly curly curly curly curly curly curly curly in \ binom {[n]} {k}：\ abs {f \ cap [r + t]} \ gs r + t -1} $。这也可以被视为广义的Turán类型结果。
Let $t$, $r$, $k$ and $n$ be positive integers and $\mathcal{F}$ a family of $k$-subsets of an $n$-set $V$. The family $ \CF $ is $ r $-wise $ t $-intersecting if for any $ F_1, \ldots, F_r \in \CF $, we have $ \abs{\cap_{i = 1}^{r}F_i}\gs t $. An $ r $-wise $ t $-intersecting family of $ r + 1 $ sets $ \{T_1, \ldots, T_{r + 1}\} $ is called an $ (r + 1,t) $-triangle if $ |T_1 \cap \cdots \cap T_{r + 1}| \ls t - 1 $. In this paper, we prove that if $ n \gs n_0(r, t, k) $, then the $ r $-wise $ t $-intersecting family $ \CF \subseteq \binom{[n]}{k} $ containing the most $ (r + 1,t) $-triangles is isomorphic to $ \curlybraces{F \in \binom{[n]}{k}: \abs{F \cap [r + t]} \gs r + t - 1} $. This can also be regarded as a generalized Turán type result.
