Séminaire Lotharingien de Combinatoire, 78B.76 (2017), 12 pp.

Emily Gunawan, Gregg Musiker and Hannah Vogel

Infinite Friezes of Cluster Algebras from Surfaces

Abstract. Originally studied by Conway and Coxeter, friezes appeared in various recreational mathematics publications in the 1970s. More recently, in 2015, Baur, Parsons, and Tschabold constructed periodic infinite friezes and related them to matching numbers in the once-punctured disk and annulus. In this paper, we study such infinite friezes with an eye towards cluster algebras of type D and affine A, respectively. By examining infinite friezes with Laurent polynomials entries, we discover new symmetries and formulas relating the entries of this frieze to one another.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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