Tutte seminar - Peter Nelson

Exponentially Dense Matroids

Abstract: 

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.