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

authored by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Universite de Reims Champagne-Ardenne

Type

Preprint

No. of pages

32

Publication date

06.04.2023

Publication status

E-pub ahead of print

Electronic version(s)

https://doi.org/10.48550/arXiv.2304.03071 (Access: Open)