Bose–Burton type theorems for finite Grassmannians

In this paper both blocking sets with respect to the s -subspaces and covers with t -subspaces in a finite Grassmannian are investigated, especially focusing on geometric descriptions of blocking sets and covers of minimum size. When such a description exists, it is called a Bose–Burton type theorem. The canonical example of a blocking set with respect to the s -subspaces is the intersection of s linear complexes. In some cases such an intersection is a blocking set of minimum size, that can occasionally be characterized by a Bose–Burton type theorem. In particular, this happens for the 1-blocking sets of the Grassmannian of planes of PG ( 5 , q ) .