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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.10521 |
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| _version_ | 1866912264132493312 |
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| author | Mabilat, Flavien |
| author_facet | Mabilat, Flavien |
| contents | A $λ$-quiddity of size $n$ is an $n$-tuple of elements from a fixed set, which is a solution to a matrix equation that arises in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion of irreducibility. The main objective of this text is to demonstrate that there is a finite number of irreducible $λ$-quiddities over a finite unitary commutative ring and to obtain in this case an upper bound for their maximal size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finiteness of the number of irreducible $λ$-quiddities over a finite commutative and unitary ring Mabilat, Flavien Combinatorics A $λ$-quiddity of size $n$ is an $n$-tuple of elements from a fixed set, which is a solution to a matrix equation that arises in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion of irreducibility. The main objective of this text is to demonstrate that there is a finite number of irreducible $λ$-quiddities over a finite unitary commutative ring and to obtain in this case an upper bound for their maximal size. |
| title | Finiteness of the number of irreducible $λ$-quiddities over a finite commutative and unitary ring |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.10521 |