Thursday, November 21, 2019

**Speaker**: Miklós Bóna

**Title:** "A method to prove that the solution to some enumeration problems is a non-rational generating function"

**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.

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