Cluster algebraic interpretation of infinite friezes

Emily Gunawan, Gregg Musiker, Hannah Vogel

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 polynomial entries, we discover new symmetries and formulas relating the entries of this frieze to one another. Lastly, we also present a correspondence between Broline, Crowe and Isaacs's classical matching tuples and combinatorial interpretations of elements of cluster algebras from surfaces.

Original languageEnglish (US)
Pages (from-to)22-57
Number of pages36
JournalEuropean Journal of Combinatorics
StatePublished - Oct 2019

Bibliographical note

Funding Information:
E. Gunawan and G. Musiker were supported by NSF, USA Grants DMS-1148634 and DMS-1362980 . H. Vogel was supported by the Austrian Science Fund (FWF) : projects No. P25141-N26 and W1230 , and acknowledges support from NAWI Graz. She would also like to thank the University of Minnesota for hosting her during her stay in the Winter of 2016.

Publisher Copyright:
© 2019 Elsevier Ltd


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