## A method to prove that the solution to some enumeration problems is a non-rational generating function

- Oct. 23, 2020
- 3 p.m.

## Abstract

The solution of an enumeration problem is very often a generating function $F$. Some problems are too difficult for us to find the explicit form of $F$. In this talk, we will introduce a method that leads to negative results that are rare in this part of combinatorics. When our method applies, it shows that $F$ is not a rational function, which provides at least some explanation of the fact that the original enumeration problem is difficult. As an example, we will discuss a 22-year old conjecture of Zeilberger and Noonan