Inequalities for two systems of subspaces with prescribed intersections

Abstract

Let $W$ denote a linear space over a fixed field $\mathbb{F}$. We define the notions of weak $ISP$-system and weak $(u,v)$-system $\mathcal{S}=\{({\mathcal{U}}_i,{\mathcal{V}}_i):1\le i\le m\}$ of subspaces of $W$. We give upper bounds for the size of weak $ISP$-systems and weak $(u,v)$-systems.

9 pages