Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Mabilat, Flavien"'
Autor:
Mabilat, Flavien
The aim of this article is to obtain a formula giving, for a positive integer $n$, the number of roots of the $n^{th}$ continuant polynomial over a finite local ring. In particular, we will give counting formulae for the roots of the continuant over
Externí odkaz:
http://arxiv.org/abs/2407.19317
Autor:
Mabilat, Flavien
This article aims to study some $n$-tuples of elements belonging to a ring $\mathbb{Z}/N\mathbb{Z}$ related to the combinatorics of congruence subgroups of the modular group. More precisely, we will focus here on the notion of minimal monomial soluti
Externí odkaz:
http://arxiv.org/abs/2406.18188
Autor:
Mabilat, Flavien
$\lambda$-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. The study of these solutions involves in particular the use of a notion of irreducibility. The mai
Externí odkaz:
http://arxiv.org/abs/2404.10521
Autor:
Mabilat, Flavien
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. Their number and their properties are closely linked to the structure and the cardinality of t
Externí odkaz:
http://arxiv.org/abs/2402.09968
Autor:
Mabilat, Flavien
The aim of this article is to continue the study of the notion of $\lambda$-quiddity over a ring, which appeared during the study of Coxeter's friezes. For this, we will focus here on situations where the ring used can be seen as a direct product of
Externí odkaz:
http://arxiv.org/abs/2308.15848
Autor:
Mabilat, Flavien
In this note, we consider matrices similar to $X$-form matrices, which are the matrices for which only the diagonal and the anti-diagonal elements can be different from zero. First, we give a characterization of these matrices using the minimal polyn
Externí odkaz:
http://arxiv.org/abs/2308.15845
Autor:
Mabilat, Flavien
In this article, we study the classification of some natural numbers related to the combinatorics of congruence subgroups of the modular group. More precisely, we will focus here on the notion of minimal monomial solutions. These are the solutions of
Externí odkaz:
http://arxiv.org/abs/2305.15784
Autor:
Cuntz, Michael, Mabilat, Flavien
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 friezes. These can be considered on various sets with very different structures from one set to another.
Externí odkaz:
http://arxiv.org/abs/2304.03071
Autor:
Mabilat, Flavien
During his work devoted to Coxeter's friezes, M. Cuntz initiated the study of the notion of $\lambda$-quiddity and raised the problem of the study of this over some subsets of $\mathbb{C}$. The objective of this text is to bring some new elements of
Externí odkaz:
http://arxiv.org/abs/2212.03142
Autor:
Mabilat, Flavien
During the study of the Coxeter friezes, M. Cuntz defined the concept of $\lambda$-quiddity and gave the problem of studying them on some subsets of $\mathbb{C}$. The objective of this text is to carry out this study in the case of some cyclic subgro
Externí odkaz:
http://arxiv.org/abs/2206.13949