论文标题
区分对称组和相关图的动作
Distinguishing actions of symmetric groups and related graphs
论文作者
论文摘要
一组$ x $的组$ g $的差异数字$ d（g，x）是$ x $的分区的最小尺寸，因此，$ g $的$ g $的元素没有在$ x $上进行非琐事的元素保留此分区。在本文中，我们描述了对称组$ s_n $的所有操作的区别数字，对于任何$ n \ geq 3 $。这使我们能够描述所有图形的差异数，其自动形态组是与对称组的同构。我们的描述解决了有关此主题的早期论文中各种作者提出的一些开放问题。
The distinguishing number $D(G,X)$ of an action of a group $G$ on a set $X$ is the least size of a partition of $X$ such that no element of $G$ acting nontrivially on $X$ preserves this partition. In this paper we describe the distinguishing numbers for all actions of the symmetric group $S_n$, for any $n\geq 3$. This allows us to describe the distinguishing numbers for all graphs whose automorphism group is isomorphic with a symmetric group. Our description solves a few open problems posed by various authors in earlier papers on this topic.
