A common generalization of hypercube partitions and ovoids in polar spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-17 DOI:10.1007/s10623-024-01489-5

Jozefien D’haeseleer, Ferdinand Ihringer, Kai-Uwe Schmidt

引用次数: 0

Abstract

We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace contains precisely one member of that family. This is a generalization of ovoids in polar spaces as well as the natural q-analog of a subcube partition of the hypercube (which can be seen as a polar space with \(q=1\)). Our main result proves that a generalized ovoid of k-spaces in polar spaces of large rank does not exist.

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极地空间中的超立方体分区和卵形体的通用概括

我们研究所谓的广义敖包，即有限经典极性空间的完全各向同性子空间族，使得每个最大完全各向同性子空间恰好包含该族的一个成员。这是极性空间中的敖包的广义化，也是超立方体的子立方体分区的自然 q-analog （可以看作是具有（q=1\）的极性空间）。我们的主要结果证明了在大秩的极空间中不存在k空间的广义卵形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.