Generalised core partitions and Diophantine equations
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911163860647936 |
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| author | Brunat, Olivier Chapelier-Laget, Nathan Gerber, Thomas |
| author_facet | Brunat, Olivier Chapelier-Laget, Nathan Gerber, Thomas |
| contents | We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense of [CLG22]. In this paper, we first develop the theory for extended affine Weyl groups. In a series of applications, we give some remarkable parametrisations of the solutions of certain Diophantine equations resembling Pell's equation, by refining the results of [BN22] and [Alp14], and generalising them to further types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised core partitions and Diophantine equations Brunat, Olivier Chapelier-Laget, Nathan Gerber, Thomas Combinatorics Number Theory Representation Theory 05E10, 11D09, 17B22, 17B67 We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense of [CLG22]. In this paper, we first develop the theory for extended affine Weyl groups. In a series of applications, we give some remarkable parametrisations of the solutions of certain Diophantine equations resembling Pell's equation, by refining the results of [BN22] and [Alp14], and generalising them to further types. |
| title | Generalised core partitions and Diophantine equations |
| topic | Combinatorics Number Theory Representation Theory 05E10, 11D09, 17B22, 17B67 |
| url | https://arxiv.org/abs/2403.11191 |