1. Packings and Steiner systems in polar spaces
- Author
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Schmidt, Kai-Uwe and Weiß, Charlene
- Subjects
FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) - Abstract
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., Comment: 25 pages; this revision contains a strengthened version of Cor. 3.4, and also small changes taking into account referee comments
- Published
- 2023