Frieze patterns with coefficients

(Joint work with M. Cuntz and P. Jorgensen) Frieze patterns, as introduced by Coxeter in the 1970’s, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpublished manuscript by Propp. In this talk I will report on a systematic study of these frieze patterns with coefficients and their fundamental properties, generalizing classic results for frieze patterns. As a consequence, frieze patterns with coefficients can be obtained from classic frieze patterns by cutting out subpolygons from the triangulated polygons associated to classic Conway-Coxeter frieze patterns. We address the question of which frieze patterns with coefficients can be obtained in this way and present a complete solution of this problem for triangles.