In combinatorics on words, for two finite words u and v, the binomial coefficient of u and v is the number of times v appears as a subsequence of u (also called (scattered) subword). For example, with u = alphalpha and v = al, there are = 36 ways to select 2 2 letters among 9, but only 3 of them give back v. Generalizing famous binomial coefficient...
La physique-chimie est une matière qui fait son apparition dès le collège. Comme la plupart des matières scientifiques, cette discipline requiert des compétences mathématiques, il s’agit d’une matière pluridisciplinaire. L’utilisation des outils mathématiques est un indispensable en science-physique. Les élèves ont parfois beaucoup de mal à disting...
We study normalisation as a rewriting system in the framework of two-way alternate bases. In this framework, nonnegative real numbers are represented by right-infinite words with a decimal point. A number may have multiple representations, among which one is distinguished unsing a greedy algorithm and called the expansion. The problem of normalisat...
In combinatorics on words, the well-studied factor complexity function $\rho_{\bf x}$ of a sequence ${\bf x}$ over a finite alphabet counts, for any nonnegative integer $n$, the number of distinct length-$n$ factors of ${\bf x}$. In this paper, we introduce the \emph{reflection complexity} function $r_{\bf x}$ to enumerate the factors occurring in ...
Deux visions s’opposent concernant les objectifs principaux de l’enseignement préscolaire, la manière dont les jeunes enfants apprennent et les pratiques pédagogiques à privilégier (Russell, 2011). Ces deux visions semblent avoir une incidence sur la conceptualisation et la mesure des connaissances pédagogiques de contenu (PCK - pedagogical content...
peer reviewed / In the context of fundamental flow studies, experimental databases are expected to provide uncertainty margins on the measured quantities. With the rapid increase in available computational power and the development of high-resolution fluid simulation techniques, Direct Numerical Simulation and Large Eddy Simulation are increasingly...
Automorphisms of the free group can be classified using their index. A maximal index indicates that the automorphism is rich as it would be geometric or parageometric. Geometric group automorphisms have been widely studied and are generated "easily". This cannot be said for parageometric automorphisms. Or could it be ?! The aim of the presentation ...
