Growth of infinite frieze patterns of affine type
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866914413571735552 |
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| author | Baur, Karin Felikson, Anna Prasad, Deepanshu Tumarkin, Pavel Yıldırım, Emine |
| author_facet | Baur, Karin Felikson, Anna Prasad, Deepanshu Tumarkin, Pavel Yıldırım, Emine |
| contents | We analyse the growth coefficients of infinite frieze patterns arising from cluster algebras using cluster modular groups and cluster categories. For a fixed cluster category of affine type, we prove that the collection of infinite frieze patterns given by both the homogeneous and non-homogeneous stable tubes all have the same growth coefficients. We also derive and verify an explicit formula for the $k$-th growth coefficient, expressed directly in terms of data from homogeneous tubes, or, alternatively, from appropriate elements of the corresponding cluster algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21157 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Growth of infinite frieze patterns of affine type Baur, Karin Felikson, Anna Prasad, Deepanshu Tumarkin, Pavel Yıldırım, Emine Combinatorics Representation Theory 13F60, 05E10, 16G20, 16G70 We analyse the growth coefficients of infinite frieze patterns arising from cluster algebras using cluster modular groups and cluster categories. For a fixed cluster category of affine type, we prove that the collection of infinite frieze patterns given by both the homogeneous and non-homogeneous stable tubes all have the same growth coefficients. We also derive and verify an explicit formula for the $k$-th growth coefficient, expressed directly in terms of data from homogeneous tubes, or, alternatively, from appropriate elements of the corresponding cluster algebra. |
| title | Growth of infinite frieze patterns of affine type |
| topic | Combinatorics Representation Theory 13F60, 05E10, 16G20, 16G70 |
| url | https://arxiv.org/abs/2603.21157 |