Growth-Rates of Matroid Classes
For a minor-closed class of matroids, we consider the maximum number, h(n), of elements in a simple rank-n matroid in the class. This growth-rate function, when finite, is known to be either linear, quadratic, or exponential. For exponentially dense classes we determine h(n) precisely, for sufficiently large n, and also describe the extremal matroids in the class. This is joint work with Peter Nelson.