论文标题
2相反排列
2-intersecting permutations
论文作者
论文摘要
在本文中，我们将ERDőS-KO-RADO属性均使用$ 2 $ - Pointwise和$ 2 $ -SETWISEWISE的相交排列。如果存在$ t $ t $ -subset $ s $ of $ \ \ {1,2，\ dots，n \} $，则两个排列$σ，τ\ sym（n）$中的相交是$ t $ - set的相交。如果对于s $中的每个$ s \，$ s^σ= s^τ$，那么我们说$σ$和$τ$是$ t $ - 点 - 点相交。我们说$ sym（n）$具有$ t $ setwise（resp。$ t $ - 点）相交的属性，如果任何家庭$ \ mathcal {f} $ of $ t $ setwise（resp。$ t $ t $ - pointwise）相交的排列，$ | \ nathcal {f} f} | \ leq（n-t）！埃利斯（[“ setwise与排列的家族相交”。埃利斯还结合了所有$ n \ geq t $的结果。 Ellis，Friedgut和Pilpel [Ellis，David，Ehud Friedgut和Haran Pilpel。 “与排列的家庭相交。” {美国数学协会期刊} 24（3）：649-682，2011。]还证明，对于$ n $，相对于$ t $，$ t $，$ sym（n）$具有$ t $ point-point-pointsince cootsectisect。还猜想$ sym（n）$具有$ n \ geq 2t+1 $的$ t $ pointwise相交propoperty。在这项工作中，当$ t = 2 $时，我们证明了这两个猜想。
In this paper we consider the Erdős-Ko-Rado property for both $2$-pointwise and $2$-setwise intersecting permutations. Two permutations $σ,τ\in Sym(n)$ are $t$-setwise intersecting if there exists a $t$-subset $S$ of $\{1,2,\dots,n\}$ such that $S^σ= S^τ$. If for each $s\in S$, $s^σ= s^τ$, then we say $σ$ and $τ$ are $t$-pointwise intersecting. We say that $Sym(n)$ has the $t$-setwise (resp. $t$-pointwise) intersecting property if for any family $\mathcal{F}$ of $t$-setwise (resp. $t$-pointwise) intersecting permutations, $|\mathcal{F}| \leq (n-t)!t!$ (resp. $|\mathcal{F}| \leq (n-t)!$). Ellis (["Setwise intersecting families of permutation". { Journal of Combinatorial Theory, Series A}, 119(4):825-849, 2012.]), proved that for $n$ sufficiently large relative to $t$, $Sym(n)$ has the $t$-setwise intersecting property. Ellis also conjuctured that this result holds for all $n \geq t$. Ellis, Friedgut and Pilpel [Ellis, David, Ehud Friedgut, and Haran Pilpel. "Intersecting families of permutations." {Journal of the American Mathematical Society} 24(3):649-682, 2011.] also proved that for $n$ sufficiently large relative to $t$, $Sym(n)$ has the $t$-pointwise intersecting property. It is also conjectured that $Sym(n)$ has the $t$-pointwise intersecting propoperty for $n\geq 2t+1$. In this work, we prove these two conjectures for $Sym(n)$ when $t=2$.
