A product theorem for $r$-cross intersecting families of subspaces

Toshihiro Shimizu, Norihide Tokushige

Let $V$ be an $n$-dimensional vector space over a finite field of order $q$. Let $r\ge 3$, $(r-1)n\ge rk$ and let $\mathcal F_1,\ldots,\mathcal F_r\subset \genfrac{[}{]}{0pt}{}{V…