Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.03071 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916672185565184 |
|---|---|
| author | Cuntz, Michael Mabilat, Flavien |
| author_facet | Cuntz, Michael Mabilat, Flavien |
| contents | The $λ$-quiddities of size $n$ are $n$-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter's friezes. These can be considered on various sets with very different structures from one set to another. The main objective of this text is to obtain explicit formulas giving the number of $λ$-quiddities of size $n$ over finite fields and over the rings $\mathbb{Z}/N\mathbb{Z}$ with $N=4m$ and $m$ square free. We will also give some elements about the asymptotic behavior of the number of $λ$-quiddities verifying an irreducibility condition over $\mathbb{Z}/N\mathbb{Z}$ when $N$ goes to the infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03071 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comptage des quiddit{é}s sur les corps finis et sur quelques anneaux $\mathbb{Z}/N\mathbb{Z}$ Cuntz, Michael Mabilat, Flavien Combinatorics The $λ$-quiddities of size $n$ are $n$-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter's friezes. These can be considered on various sets with very different structures from one set to another. The main objective of this text is to obtain explicit formulas giving the number of $λ$-quiddities of size $n$ over finite fields and over the rings $\mathbb{Z}/N\mathbb{Z}$ with $N=4m$ and $m$ square free. We will also give some elements about the asymptotic behavior of the number of $λ$-quiddities verifying an irreducibility condition over $\mathbb{Z}/N\mathbb{Z}$ when $N$ goes to the infinity. |
| title | Comptage des quiddit{é}s sur les corps finis et sur quelques anneaux $\mathbb{Z}/N\mathbb{Z}$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2304.03071 |