On the Frankl--Tokushige conjecture and almost complete $r$-cross $t$-intersection theorems for vector spaces

Yao Li, Benjian Lv, Jie Wen

Let $r\ge 3$ and $k_1\ge k_2\ge \cdots \ge k_r\ge t$. Let ${\mathcal{F}}_1,{\mathcal{F}}_2,\dots ,{\mathcal{F}}_r$ be families of subspaces, of respective dimensions $k_1,k_2,\ldots,k_…