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Friezes, weak friezes, and T-paths

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Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluster variables. This paper will introduce the concepts of weak friezes and T-paths with respect to dissections of polygons. Our main result is that weak friezes are characterised by satisfying an expansion formula which we call the T-path formula. We also show that weak friezes can be glued together, and that the resulting weak frieze is a frieze if and only if so was each of the weak friezes being glued.

Original languageEnglish
Article number102253
JournalAdvances in Applied Mathematics
Publication statusPublished - Oct 2021

Bibliographical note

Publisher Copyright:
© 2021 The Authors

    Research areas

  • Cluster algebra, Cluster expansion formula, Frieze pattern, Generalised frieze pattern, Polygon dissection, Positivity, Semifield

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