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 ${\mathcal{A}}_1,{\mathcal{A}}_2,\dots$, 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…