It has been known that several objects such as cluster variables, coefficients, seeds, and $Y$‐seeds in different cluster patterns with common exchange matrices share the same periodicity under mutations. We call it synchronicity phenomenon in cluster patterns. In this expository note we explain the mechanism of synchronicity based on several fundamental results on cluster algebra theory such as separation formulas, sign‐coherence, Laurent positivity, duality, and detropicalization obtained by several authors. We also show that all synchronicity properties studied in this paper are naturally extended to cluster patterns of generalized cluster algebras, up to the Laurent positivity conjecture.

中文翻译：

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集群模式中的同步现象

众所周知，有几个对象，例如聚类变量，系数，种子和 $ÿ$具有不同交换矩阵的不同簇模式的种子在突变下具有相同的周期性。我们称其为集群模式中的同步现象。在此说明性注释中，我们基于几位作者关于群集代数理论的一些基本结果（例如分离公式，符号相干性，Laurent正性，对偶性和去热带化）来解释同步机制。我们还表明，本文研究的所有同步性都自然地扩展到广义簇代数的簇模式，直至Laurent正猜想。