论文标题
用点和超平面阻止子空间
Blocking subspaces with points and hyperplanes
论文作者
论文摘要
在本文中，我们表征了最小的$ b $由$ \ text {pg}（n，q）$组成的点和超级平面的$，因此每个$ k $ -space均以$ b $的至少一个元素的元素事件。如果$ k> \ frac {n-1} 2 $，则最小的结构仅由点组成。双重，如果$ k <\ frac {n-1} 2 $，最小的示例仅由超平面组成。但是，如果$ k = \ frac {n-1} 2 $，则存在包含点和超平面的集合，它们比仅包含点或仅包含超平面的任何阻止集小。
In this paper, we characterise the smallest sets $B$ consisting of points and hyperplanes in $\text{PG}(n,q)$, such that each $k$-space is incident with at least one element of $B$. If $k > \frac {n-1} 2$, then the smallest construction consists only of points. Dually, if $k < \frac{n-1}2$, the smallest example consists only of hyperplanes. However, if $k = \frac{n-1}2$, then there exist sets containing both points and hyperplanes, which are smaller than any blocking set containing only points or only hyperplanes.
