Radius-zero Extended Symmetries and Irregular Fibres of ${\mathbb{Z}}^d$-Substitution Subshifts

Álvaro Bustos-Gajardo, Daniel Luz, Neil Mañibo

In this work, we consider ${\mathbb{Z}}^d$-shifts generated by digit substitutions. For such a shift $\mathbb{X}$, we study the elements of the normaliser of ${\mathbb{Z}}^d$ in the gr…