A flag of a finite set S is a set f of non-empty proper subsets of S such that $A\subseteq B$ or $B\subseteq A$ for all $A,B\in f$. The set $\{|A|:A\in f\}$ is called the type of f. Two flags f and $f^{\prime }$ are in general position (with respect to S) when $A\cap B=\varnothing$ or $A\cup B=S$ for all $A\in f$ and $B\in f^{\prime }$. We study sets of flags of a fixed type T that are mutually not in general position and are interested in the largest cardinality of these sets. This is a generalization of the classical Erdős-Ko-Rado problem. We will give some basic facts and determine the largest cardinality in several non-trivial cases. For this we will define graphs whose vertices are flags and the problem is to determine the independence number of these graphs.

有限集S的标志是S的非空真子集的集合f使得$\mathrm{一个}\subseteq 乙$或者$乙\subseteq \mathrm{一个}$对所有人$\mathrm{一个},乙\in F$. 套装$\{|\mathrm{一个}|：\mathrm{一个}\in F\}$称为f的类型。两个标志f和$F^{\text{'}}$处于一般位置（相对于S）时$\mathrm{一个}\cap 乙=\varnothing$或者$\mathrm{一个}\cup 乙=\mathrm{小号}$对所有人$\mathrm{一个}\in F$和$乙\in F^{\text{'}}$. 我们研究固定类型T的标志集，它们相互不在一般位置，并且对这些集的最大基数感兴趣。这是经典 Erdős-Ko-Rado 问题的推广。我们将给出一些基本事实并确定几个非平凡案例中的最大基数。为此，我们将定义顶点为标志的图，问题是确定这些图的独立数。