Infinite friezes of cluster algebras from surfaces

Emily Gunawan, Gregg Musiker, Hannah Vogel

Research output: Contribution to conferencePaperpeer-review

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.

Original languageEnglish (US)
StatePublished - 2006
Event29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom
Duration: Jul 9 2017Jul 13 2017

Conference

Conference29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
CountryUnited Kingdom
CityLondon
Period7/9/177/13/17

Bibliographical note

Funding Information:
∗E. Gunawan and G. Musiker were supported by NSF Grants DMS-1148634 and DMS-1362980. Vogel was supported by the Austrian Science Fund (FWF): projects No. P25141-N26 and W1230.

Keywords

  • Cluster algebra
  • Conway-Coxeter frieze
  • Marked surface
  • Triangulation

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