论文标题
极地空间中的包装和坦Steiner系统
Packings and Steiner systems in polar spaces
论文作者
论文摘要
等级$ n $的有限古典极性空间由有限矢量空间的完全各向同性子空间组成，配备有非排定形式，因此$ n $是这种子空间的最大维度。在有限的古典极性空间中，$ t $ steiner系统是一个完全奇异$ n $空间的$ y $ y $，因此每个$ y $的一位成员都包含每个完全奇异$ t $ - 空间。非平凡的例子仅以$ t = 1 $而闻名，$ t = n-1 $。我们对此类$ T $ steiner系统进行了几乎完整的分类，表明只有在某些角落情况下才能存在此类对象。此分类结果是由于对极性空间中的包装的更一般结果。
A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces.
