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.

中文翻译：

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饰带、弱饰带和 T 形路径

楣图案形成了代数、组合学和几何之间的联系。关于表面三角剖分的T路径已被用于获得集群变量的扩展公式。

本文将介绍有关多边形解剖的弱带和T路径的概念。我们的主要结果是弱带的特征在于满足我们称为T路径公式的扩展公式。

我们还表明，弱楣可以粘合在一起，并且当且仅当每个弱楣被粘合在一起时，由此产生的弱楣是楣。