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arXiv · 2005.06230

Friezes, weak friezes, and T-paths

Ilke Canakci·Peter Jorgensen
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Abstract

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.

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Ilke Canakci, Peter Jorgensen. 2020-05-13. Friezes, weak friezes, and T-paths. https://arxiv.org/abs/2005.06230

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