Cluster algebraic interpretation of infinite friezes

Emily Gunawan; Gregg Musiker; Hannah Vogel

doi:10.1016/j.ejc.2019.04.002

Cluster algebraic interpretation of infinite friezes

Emily Gunawan, Gregg Musiker, Hannah Vogel

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 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 language	English (US)
Pages (from-to)	22-57
Number of pages	36
Journal	European Journal of Combinatorics
Volume	81
DOIs	https://doi.org/10.1016/j.ejc.2019.04.002
State	Published - Oct 2019

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© 2019 Elsevier Ltd

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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 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.",

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doi = "10.1016/j.ejc.2019.04.002",

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AU - Musiker, Gregg

AU - Vogel, Hannah

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AB - 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.

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ER -

Cluster algebraic interpretation of infinite friezes

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