Comptage des quiddités sur les corps finis et sur quelques anneaux ℤ/Nℤ

verfasst von

Michael Cuntz, Flavien Mabilat

Abstract

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 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 ℤ/Nℤ 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 ℤ/Nℤ when N goes to the infinity.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Universite de Reims Champagne-Ardenne

Typ

Preprint

Anzahl der Seiten

32

Publikationsdatum

06.04.2023

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2304.03071 (Zugang: Offen)