Friezes and continuant polynomials with parameters

Véronique Bazier-Matte; David Racicot-Desloges; Tanna Sanchez

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arXiv · 1404.0045

Friezes and continuant polynomials with parameters

Véronique Bazier-Matte·David Racicot-Desloges·Tanna Sanchez

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Abstract

Frieze patterns (in the sense of Conway and Coxeter) are related to cluster algebras of type A and to signed continuant polynomials. In view of studying certain classes of cluster algebras with coefficients, we extend the concept of signed continuant polynomial to define a new family of friezes, called c-friezes, which generalises frieze patterns. Having in mind the cluster algebras of finite type, we identify a necessary and sufficient condition for obtaining periodic c-friezes. Taking into account the Laurent phenomenon and the positivity conjecture, we present ways of generating c-friezes of integers and of positive integers. We also show some specific properties of c-friezes.

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BibTeX RIS

Véronique Bazier-Matte, David Racicot-Desloges, Tanna Sanchez. 2014-03-31. Friezes and continuant polynomials with parameters. https://arxiv.org/abs/1404.0045

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