Friezes, Strings and Cluster Variables

Abstract

To any walk in a quiver, we associate a Laurent polynomial. When the walk is the string of a string module over a 2-Calabi-Yau tilted algebra, we prove that this Laurent polynomial coincides with the corresponding cluster character of the string module, up to an explicit normalising monomial factor.

Some minor typos were fixed and some sections were shortened; to appear in Glasgow Mathematical Journal (2011) 32 pages