Frieze patterns over finite commutative local rings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917829384601600 |
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| author | Böhmler, Bernhard Cuntz, Michael |
| author_facet | Böhmler, Bernhard Cuntz, Michael |
| contents | We count numbers of tame frieze patterns with entries in a finite commutative local ring. For the ring $\mathbb{Z}/p^r\mathbb{Z}$, $p$ a prime and $r\in\mathbb{N}$ we obtain closed formulae for all heights. These may be interpreted as formulae for the numbers of certain relations in quotients of the modular group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frieze patterns over finite commutative local rings Böhmler, Bernhard Cuntz, Michael Combinatorics Group Theory 20H05, 05E99, 13F60, 51M20 We count numbers of tame frieze patterns with entries in a finite commutative local ring. For the ring $\mathbb{Z}/p^r\mathbb{Z}$, $p$ a prime and $r\in\mathbb{N}$ we obtain closed formulae for all heights. These may be interpreted as formulae for the numbers of certain relations in quotients of the modular group. |
| title | Frieze patterns over finite commutative local rings |
| topic | Combinatorics Group Theory 20H05, 05E99, 13F60, 51M20 |
| url | https://arxiv.org/abs/2407.12596 |