Clustering Cluster Algebras with Clusters
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918334794039296 |
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| author | Cheung, Man-Wai Dechant, Pierre-Philippe He, Yang-Hui Heyes, Elli Hirst, Edward Li, Jian-Rong |
| author_facet | Cheung, Man-Wai Dechant, Pierre-Philippe He, Yang-Hui Heyes, Elli Hirst, Edward Li, Jian-Rong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09771 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Clustering Cluster Algebras with Clusters Cheung, Man-Wai Dechant, Pierre-Philippe He, Yang-Hui Heyes, Elli Hirst, Edward Li, Jian-Rong High Energy Physics - Theory Combinatorics 13F60, 05E10 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. |
| title | Clustering Cluster Algebras with Clusters |
| topic | High Energy Physics - Theory Combinatorics 13F60, 05E10 |
| url | https://arxiv.org/abs/2212.09771 |