5 papers · 1 filter
Pairs of square-free arithmetic progressions in infinite words
Thomas Delépine, Pascal Ochem, Matthieu Rosenfeld
We study a question of Harju from 2019 regarding the existence of infinite ternary square-free words whose subsequences modulo and are also square-free for relatively prime…
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 , there exists a cube-free word so that $c_1\in\mathcal{A}_1,c_2\in\mathcal{A}_2…
Words avoiding the morphic images of most of their factors
Pascal Ochem, Matthieu Rosenfeld
We say that a finite factor of a word is \emph{imaged} if there exists a non-erasing morphism , distinct from the identity, such that contains . We show that e…
An explicit condition for boundedly supermultiplicative subshifts
Vuong Bui, Matthieu Rosenfeld
We study some properties of the growth rate of , that is, the language of words over the alphabet avoiding the set of forbidden…
On Vizing's problem for triangle-free graphs
Ross J. Kang, Matthieu Rosenfeld
We prove that for any triangle-free graph of maximum degree provided . This gives tangible progress towards an old problem of Vi…