Frieze Patterns from Dissections

Abstract: Finite frieze patterns of positive integers were shown by Conway and Coxeter to be in bijection with triangulated polygons. Baur, Parsons, and Tschabold generalized this result, showing that infinite frieze patterns of positive integers are in bijection with triangulated annuli and once-punctured discs. More recently, Holm and Jørgensen investigated frieze patterns arising from dissected polygons. The frieze patterns of Holm and Jørgensen involve algebraic integers of the form 2cos(pi/p) for an integer p. We combine these generalizations and present results on frieze patterns from dissected annuli, using these same algebraic integers. We also discuss how some of these frieze patterns from dissections can be connected to generalized cluster algebras, in the sense of Chekhov and Shapiro. This is based on joint work with Jiuqi (Lena) Chen and with Elizabeth Kelley.

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)