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arXiv · 2203.06709

Packings and Steiner systems in polar spaces

Kai-Uwe Schmidt·Charlene Weiß
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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.

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Kai-Uwe Schmidt, Charlene Weiß. 2022-03-13. Packings and Steiner systems in polar spaces. https://arxiv.org/abs/2203.06709

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