3 citations · 8 across the 13 of their papers we have counts for
14 papers · 1 filter
Une curieuse égalité entre deux sommes de produits de coefficients binomiaux
Flavien Mabilat
We will show in this text that, for all non-negative integers and , the following equality is verified: \[\sum_{i=0}^{l} {n-i \choose i}{l+i \choose 2i+1}=\sum_{i=0}^{l} {n-…
Étude de quelques familles de -quiddités et minoration de la taille maximale des -quiddités irréductibles sur un corps fini
Flavien Mabilat
-quiddities of size are -tuples of elements from a fixed set that are solutions to a matrix equation which is fundamental in the study of the combinatorics of the modular…
Éléments de comptage sur les générateurs du groupe modulaire et les -quiddités
Flavien Mabilat
The aim of this article is to count the -tuples of positive integers solutions of the equation $\begin{pmatrix} a_{n} & -1 \\[4pt] 1 & 0 \end{pmatrix} \be…
Étude des liens entre la taille et l'irréductibilité des solutions monomiales minimales dans
Flavien Mabilat
This article aims to study some -tuples of elements belonging to a ring related to the combinatorics of congruence subgroups of the modular group. More…
-quiddités sur des produits directs d'anneaux
Flavien Mabilat
The aim of this article is to continue the study of the notion of -quiddity over a ring, which appeared during the study of Coxeter's friezes. For this, we will focus here on si…
Classification des entiers monomialement irr{é}ductibles et g{é}n{é}ralisations
Flavien Mabilat
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 o…
Comptage des quiddit{é}s sur les corps finis et sur quelques anneaux
Michael Cuntz, Flavien Mabilat
The -quiddities of size are -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 var…
-quiddit{é} sur certains sous-groupes monog{è}nes de
Flavien Mabilat
During the study of Coxeter's friezes, M. Cuntz defined the concept of -quiddities and gave the problem of studying them over some subsets of . The objective of this…
Solutions monomiales minimales irréductibles dans
Flavien Mabilat
In this article, we study the combinatorics of congruence subgroups of the modular group. More precisely, we consider the notion of minimal monomial solutions. These are the soluti…
Entiers monomialement irr{é}ductibles
Flavien Mabilat
In this article we study the combinatorics of congruence subgroups of the modular group. We consider the notion of minimal monomial solutions. These are the solutions of a matrix e…
Combinatoire des Sous-Groupes de Congruence du Groupe Modulaire II
Flavien Mabilat
In this paper, we study combinatorics of congruence subgroups of the modular group. More precisely, we consider the matrix equation that naturally arises in the theory of Coxeter f…
-quiddit{é} sur avec transcendant
Flavien Mabilat
As part of the study of Coxeter's friezes, M. Cuntz introduced the notion of irreducible -quiddity cycle. The objective of this note is to list all the irreducible -quiddity…
Combinatoire des sous-groupes de congruence du groupe modulaire
Flavien Mabilat
In this paper, we study the combinatorics of congruence subgroups of the modular group by generalizing results obtained in the non-modular case. For this, we define a notion of irr…
Quelques éléments de combinatoire des matrices de
Flavien Mabilat
A Theorem of V.Ovsienko characterizes sequences of positive integers such that the -matrix $\begin{pmatrix} a_n & -1 \\ 1 & 0 \end{pmatrix}\cdots…