Size functions of subgeometry-closed classes of representable combinatorial geometries

Let exq(G; n) be the maximum number of points in a rank-n geometry (simple matroid) that is representable over GF(q) and that has no restriction isomorphic to the geometry G. We find exq(G; n) for several infinite families of geometries G, and we show that if G is a binary affine geometry, then lim n ex2(G; n) 2n - 1 = 0.

• Type: Journal
• Year: 2000
• Where: DM
• Authors: Joseph E. Bonin, Hongxun Qin
• Keywords: DM 2000, Geometry G, Maximum Number, Rank-n Geometry