A new approach to the $2$-regularity of the $\ell$-abelian complexity of $2$-automatic sequences

Aline Parreau, Michel Rigo, Eric Rowland +1

We prove that a sequence satisfying a certain symmetry property is $2$-regular in the sense of Allouche and Shallit, i.e., the $\mathbb{Z}$-module generated by its $2$-kernel is fi…