Suboptimal $s$-union familes and $s$-union antichains for vector spaces

Yunjing Shan, Junling Zhou

Let $V$ be an $n$-dimensional vector space over the finite field ${\mathbb{F}}_q$, and let $\mathcal{L}(V)={\bigcup }_{0\le k\le n}\left[\genfrac{}{}{0ex}{}{V}{k}\right]$ be the set of all subspaces…