## UConn Math Club

# Counting Trees

## Jeremy Teitelbaum (University of Connecticut)

### Wednesday, February 28, 2018
5:45 pm

MONT 321

A tree is a collection of dots connected by lines so that there is exactly one path between any pair of dots. Trees arise in many parts of applied and pure mathematics, as well as in statistics, computer science, and mathematical biology. In this talk I will explore the problem of counting the number of trees that can be built from a given number of dots, and show how the problem changes as you add and remove different conditions on the structure of the tree. For example, a rooted tree is a tree with one dot marked as special. The picture below shows the 9 rooted trees on five dots, with the special dot drawn at the top. How many such trees are there with six dots?

**Comments: **Free pizza and drinks!