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arXiv · 2304.03071

Comptage des quiddit{\'e}s sur les corps finis et sur quelques anneaux $\mathbb{Z}/N\mathbb{Z}$

Michael Cuntz·Flavien Mabilat
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Abstract

The $\lambda$-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 $\lambda$-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 $\lambda$-quiddities verifying an irreducibility condition over $\mathbb{Z}/N\mathbb{Z}$ when $N$ goes to the infinity.

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Michael Cuntz, Flavien Mabilat. 2023-04-06. Comptage des quiddit{\'e}s sur les corps finis et sur quelques anneaux $\mathbb{Z}/N\mathbb{Z}$. https://arxiv.org/abs/2304.03071

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