论文标题
与集群的聚类集群代数
Clustering Cluster Algebras with Clusters
论文作者
论文摘要
群集代数中群集变量的分类（尤其是格拉斯曼尼亚群集代数）是一个重要的问题，它直接应用于物理中散射幅度的计算。在本文中，我们使用Tableaux方法对Grassmannian集群代数$ \ MATHBB {C} [gr（k，n）] $最高$（k，n）=（3,12），（4,10）$，或$（4,10）$（或（4,12）$（4,12）$使用Tablaeaux，使用HPC Clusters。这些数据集可在GitHub上提供。有监督和无监督的机器学习方法用于分析这些数据并确定与群集变量相对应的与Tableaux相关的结构。提出了猜想与每个等级的列表的枚举以及借助机器学习产生集群变量的tableaux结构有关。
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scattering amplitudes in physics. In this paper, we apply the tableaux method to classify cluster variables in Grassmannian cluster algebras $\mathbb{C}[Gr(k,n)]$ up to $(k,n)=(3,12), (4,10)$, or $(4,12)$ up to a certain number of columns of tableaux, using HPC clusters. These datasets are made available on GitHub. Supervised and unsupervised machine learning methods are used to analyse this data and identify structures associated to tableaux corresponding to cluster variables. Conjectures are raised associated to the enumeration of tableaux at each rank and the tableaux structure which creates a cluster variable, with the aid of machine learning.
