On the common nature of spreads and pencils in PG(d, q) Original Research Article

Cameron and Liebler proposed the problem to determine the line sets of PG(d, q) having a fixed number of lines in common with each spread. In this paper we generalize this problem, characterizing the pairs (L, B) of line sets such that |;L ∩ g B| = c for all g ϵ PGL(d + 1, q). We shall do this more generally in the context of rank 3 permutation groups, strongy regular graphs and partial geometric designs.