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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.09219 |
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| _version_ | 1866909834893328384 |
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| author | Mabilat, Flavien |
| author_facet | Mabilat, Flavien |
| contents | $λ$-quiddities of size $n$ are $n$-tuples of elements from a fixed set that are solutions to a matrix equation which is fundamental in the study of the combinatorics of the modular group and Coxeter's friezes. To gain further insight into these objects, we use a notion of irreducibility, which allows restricting the study to a limited number of elements that must be determined for each set. Our goal here is to define several families of $λ$-quiddities over finite fields and to study their irreducibility properties, with the specific aim of establishing lower bounds on the maximal size of irreducible elements over $\mathbb{F}_{q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Étude de quelques familles de $λ$-quiddités et minoration de la taille maximale des $λ$-quiddités irréductibles sur un corps fini Mabilat, Flavien Combinatorics $λ$-quiddities of size $n$ are $n$-tuples of elements from a fixed set that are solutions to a matrix equation which is fundamental in the study of the combinatorics of the modular group and Coxeter's friezes. To gain further insight into these objects, we use a notion of irreducibility, which allows restricting the study to a limited number of elements that must be determined for each set. Our goal here is to define several families of $λ$-quiddities over finite fields and to study their irreducibility properties, with the specific aim of establishing lower bounds on the maximal size of irreducible elements over $\mathbb{F}_{q}$. |
| title | Étude de quelques familles de $λ$-quiddités et minoration de la taille maximale des $λ$-quiddités irréductibles sur un corps fini |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.09219 |