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.

The talk will be accessible to graduate students.