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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.

TidsskriftAdvances in Applied Mathematics
StatusUdgivet - okt. 2021

Bibliografisk note

Funding Information:
This work was supported by EPSRC grant EP/P016014/1 “Higher Dimensional Homological Algebra”.

Publisher Copyright:
© 2021 The Authors

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