6 papers
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-…
Ãtude 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 modula…
-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 thi…
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 va…
Ãléments 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…
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…