A Bollobás-type theorem for affine subspaces. (English) Zbl 1326.05099
Summary: Let \(W\) denote the \(n\)-dimensional affine space over the finite field \(\mathbb F_q\). We prove here a Bollobás-type upper bound in the case of the set of affine subspaces. We give a construction of a pair of families of affine subspaces, which shows that our result is almost sharp.
MSC:
05C65 | Hypergraphs |
05B35 | Combinatorial aspects of matroids and geometric lattices |
05A05 | Permutations, words, matrices |
51N15 | Projective analytic geometry |
51E15 | Finite affine and projective planes (geometric aspects) |