English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate what we call generalized ovoids, that is families of totallyisotropic subspaces of finite classical polar spaces such that each maximaltotally isotropic subspace contains precisely one member of that family. Thisis a generalization of ovoids in polar spaces as well as the natural $q$-analogof a subcube partition of the hypercube (which can be seen as a polar spacewith $q=1$). Our main result proves that a generalized ovoid of $k$-spaces inpolar spaces of large rank does not exist. More precisely, for $q=p^h$, $p$prime, and some positive integer $k$, a generalized ovoid of $k$-spaces in apolar space $\mathcal{P}$ with rank $r \geq r_0(k, p)$ in a vector space$V(n,q)$ does not exist.

A common generalization of hypercube partitions and ovoids in polar spaces