# Tutte seminar - Peter Nelson

Friday, September 12, 2014 — 3:30 PM EDT

## Exponentially Dense Matroids

Speaker: Peter Nelson University of Waterloo Mathematics 3 (M3) 3103

### 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.

Location
M3 - Mathematics 3
3103
200 University Avenue West

Waterloo, ON N2L 3G1

### January 2023

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