2022/12/19 by Man-Wai Cheung, Cheung, Man-Wai, Pierre-Philippe Dechant +9 · 4 citations
Materials Science · Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nanocluster Synthesis and Applications #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2212.09771
openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 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.