论文标题
传递基团与循环点稳定器的交点密度
Intersection density of transitive groups with cyclic point stabilizers
论文作者
论文摘要
对于置换$ v $的排列组$ g $，如果每对元素$ g，in \ mathcal {f} $，$ g $的子集$ \ mathcal {f} $ of $ g $ of $ g $ of $ g $，则是一个相交集合。传递置换组$ g $的交点密度$ρ（g）$是商$ | \ Mathcal {f} |/| g_v | $的最大值，其中$ g_v $是v $ in v $ in v $和$ \ mathcal {f} $运行的$ g_v $的稳定器。 如果$ g_v $是$ g $中最大的相交设置，那么$ g $据说具有Erdős-ko-Rado（EKR） - Property。本文专门研究了及时置换量基团的研究，其点稳定器具有质量阶的稳定器，并特别强调了订单2和3没有EKR - 培训。除其他外，给出了具有交叉密度$ 4/3 $的订单稳定器的无限置换置换组的构造，并给出了具有任意较大交叉点密度的订单$ 3 $的无限置换置换式群体的无限型家族的构造。
For a permutation group $G$ acting on a set $V$, a subset $\mathcal{F}$ of $G$ is said to be an intersecting set if for every pair of elements $g,h\in \mathcal{F}$ there exists $v \in V$ such that $g(v) = h(v)$. The intersection density $ρ(G)$ of a transitive permutation group $G$ is the maximum value of the quotient $|\mathcal{F}|/|G_v|$ where $G_v$ is a stabilizer of a point $v\in V$ and $\mathcal{F}$ runs over all intersecting sets in $G$. If $G_v$ is a largest intersecting set in $G$ then $G$ is said to have the Erdős-Ko-Rado (EKR)-property. This paper is devoted to the study of transitive permutation groups, with point stabilizers of prime order with a special emphasis given to orders 2 and 3, which do not have the EKR-property. Among other, constructions of infinite family of transitive permutation groups having point stabilizer of order $3$ with intersection density $4/3$ and of infinite families of transitive permutation groups having point stabilizer of order $3$ with arbitrarily large intersection density are given.
