Seminar

Sergey Fomin and Andrei Zelevinsky defined cluster algebras by recursively constructing their generators via a process called mutation. This process is closely related to various sequences of integers, arising for instance from Coxeter-Conway friezes, whose terms can be seen as specializations of the generators of specific cluster algebras.

Although the fact that these sequences contain only integers is sometimes surprising from their definition, the theory of cluster algebras provides a common explanation for it: the Laurent Phenomenon.

In this talk, we will first list some examples of recurrence relations of integers, then we will try to understand them from the point of view of cluster algebras.