Size functions of subgeometry-closed classes of representable combinatorial geometries Original Research Article

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, thenlimn→∞ ex2(G;n)2n−1=0.