Long mutation cycles

Abstract

A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed $n\ge 4$, we describe arbitrarily long mutation cycles involving $n$-vertex quivers. Each of these mutation cycles allows for an arbitrary choice of $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ positive integer parameters. None of the mutation cycles we construct can be paved by short mutation cycles.

41 page, 15 figures. Minor editorial changes. This is the final version, to appear in Selecta Mathematica