On $\ell$-weakly cross $t$-intersecting families for sets and vector spaces
Let $[n]$ (resp. $V$) be an $n$-element set (resp. $n$-dimensional vector space over the finite field $\mathbb{F}_{q}$), and $\binom{[n]}{k}$ (resp. $\genfrac{[}{]}{0pt}{}{V}{k}$) denote the set of all $k$-subsets of $[n]$ (resp. $k$-dimensional subspaces of $V$). We say that $\mathcal{F}\subseteq\binom{[n]}{k}$ (resp. $\mathcal{F}\subseteq \genfrac{[}{]}{0pt}{}{V}{k}$) and …