作用于$k$的$S_n$的统计数据-集
Statistics for $S_n$ acting on $k$-sets
摘要：
我们研究自然行动的$S_n$的集合$k$ -子集的集合$\{1,\dots, n\}$时，$1\leq k \leq \frac{n}{2}$。对于这个动作，我们计算最小基的最大尺寸，无冗余基的高度和最大长度。这里“基”是具有平凡逐点稳定子的集合，“高度”是具有逐点稳定子不等于任何真子集的逐点稳定子的属性的子集的最大大小，并且“非冗余基”可以被认为是所有包含都是真的（逐点）集合稳定子的链。
英文摘要：
We study the natural action of $S_n$ on the set of $k$-subsets of the set $\{1,\dots, n\}$ when $1\leq k \leq \frac{n}{2}$. For this action we calculate the maximum size of a minimal base, the height and the maximum length of an irredundant base. Here a "base" is a set with trivial pointwise stabilizer, "height" is the maximum size of a subset with the property that its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset, and an "irredundant base" can be thought of as a chain of (pointwise) set-stabilizers for which all containments are proper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
