论文标题
部分可观测时空混沌系统的无模型预测
Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations
论文作者
论文摘要
我们提供了两种新的组合方法，用于计算来自可能刺破表面的弧的集群扩展公式。首先是使用$ t $ walks，这是$ t $ path型号的扩展，用于不施加的表面到一般表面。我们还引入了一种新的方式来产生$ t $ paths。第二种方法是使用与弧相关的标记POSET的订单理想。我们还使用定向POSET的理论，以使用$ 2 $乘$ 2 $矩阵来计算表达式的快速方法。引入的技术适用于集群代数及其他地区的不同设置。
We give two new combinatorial methods for computing cluster expansion formulas for arcs coming from possibly punctured surfaces. The first is by using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to general surfaces. We also introduce a new way of generating $T$-paths. The second method is by using order ideals of labeled posets associated to arcs. We also use the theory of oriented posets to give a quick way to calculate the expressions using $2$ by $2$ matrices. The techniques introduced are applicable to different settings in cluster algebras and beyond.
