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      Friezes and continuant polynomials with parameters

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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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          Journal
          31 March 2014
          Article
          1404.0045
          d5069a5b-27dd-4256-a06b-9d8574c1a90d

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          26 pages
          math.RT

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