M. Rosenfeld

collaborators

3 papers

math.CO2025

There exist infinite cube-free words over any sequence of binary alphabets

Vuong Bui, Matthieu Rosenfeld

We prove that for any sequence of binary alphabets $A_{1}, A_{2}, \dots$ , there exists a cube-free word $c_{1} c_{2} \dots$ so that $c_1\in\mathcal{A}_1,c_2\in\mathcal{A}_2…

math.CO2025

Words avoiding the morphic images of most of their factors

Pascal Ochem, Matthieu Rosenfeld

We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$ , distinct from the identity, such that $w$ contains $m (f)$ . We show that e…

math.NT2025

Decomposing a factorial into large factors

Boris Alexeev, Evan Conway, Matthieu Rosenfeld +4

Let $t (N)$ denote the largest number such that $N!$ can be expressed as the product of $N$ integers greater than or equal to $t (N)$ . The bound $t (N) / N = 1/ e - o (1)$ was apparently es…