Monday, September 14th, 2015 | 4pm-5pm | Burnside 1205 |

University of Waterloo

Exponentially Dense Matroids

The growth rate function for a minor-closed class of matroids is the function h(n) whose value at an integer n is the maximum number of elements in a simple matroid in the class of rank at most n; this can be seen as a measure of the density of the matroids in the class. A theorem of Geelen, Kabell, Kung and Whittle implies that h(n), where finite, grows either linearly, quadratically, or exponentially with base equal to some prime power q, in n. I will discuss growth rate functions for classes of the exponential sort, determining the growth rate function almost exactly for various interesting classes and giving a theorem that essentially characterizes all such functions.