An Extremal Problem for Families of Pairs of Subspaces

We consider the following vector space analogue of problem in extremal set theory. k, l) denote the maximal t for which there exist t pairs of linear subspaces (Ui, Vi ),…,(Ui, Vi) of a real vector space H, such that dim Ui = k, dim Vi = l, Ui ∩ Vi = 0 and for any l ⩽ i ≠ j ⩽ t, either Ui ∩ Vj ≠ 0 or Uj ∩ Vi ≠ 0. shown that - o(1)) ⩽ g(l, n - 1) ⩽ (n + 12) ⩽ g(k, n - k) ⩽ c′kn2k me 0 < ck, c′k.