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

@article{Eisfeld1998OnTC,
  title={On the common nature of spreads and pencils in PG(d, q)},
  author={J{\"o}rg Eisfeld},
  journal={Discrete Mathematics},
  year={1998},
  volume={189},
  pages={95-104}
}
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 (9, 3) of line sets such that 19 n gS?l = c for all g E 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. @ 1998 Elsevier Science B.V. All rights reserved