Size functions of subgeometry-closed classes of representable combinatorial geometries

Abstract

Let ex q ( 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 ex q ( G; n) for several infinite families of geometries G, and we show that if G is a binary affine geometry, then lim n→∞ ex 2(G;n) 2 n−1 =0.