M. Rosenfeld

collaborators

6 papers

math.CO2026

Pairs of square-free arithmetic progressions in infinite words

Thomas DelÃ©pine, Pascal Ochem, Matthieu Rosenfeld

We study a question of Harju from 2019 regarding the existence of infinite ternary square-free words whose subsequences modulo $p$ and $q$ are also square-free for relatively prime…

math.NT2026

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…

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.CO2025

On Vizing's problem for triangle-free graphs

Ross J. Kang, Matthieu Rosenfeld

We prove that $I ¨ (G) \leq ⌈(I^ + 1) /2 ⌉ + 1$ for any triangle-free graph $G$ of maximum degree $I^$ provided $I^ \geq 524$ . This gives tangible progress towards an old problem o…

math.CO2025

An explicit condition for boundedly supermultiplicative subshifts

Vuong Bui, Matthieu Rosenfeld

We study some properties of the growth rate of $L (A, F)$ , that is, the language of words over the alphabet $A$ avoiding the set of forbidden…