More on r-cross t-intersecting families for vector spaces

Abstract

Let V be a finite dimensional vector space over a finite field. Suppose that $F_1$, $F_2$, …, $F_r$ are r-cross t-intersecting families of k-subspaces of V. In this paper, we determine the extremal structure when ${\prod }_{i=1}^r\left|F_i\right|$ is maximum under the condition that $\dim \left({\bigcap }_{F\in F_i}F\right)<t$ for each i.