Tilings and point sets arising from substitutions are classical mathematical models of
quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding …

In this work, we consider a class of substitutions on infinite alphabets and show that they
exhibit a growth behaviour which is impossible for substitutions on finite alphabets. While for …

We introduce qubit substitutions in $\mathbb {Z}^ m $, which have non-rectangular domains
based on an endomorphism $ Q $ of $\mathbb {Z}^ m $ and a set $\mathcal {D} $ of coset …

We study substitutions on a countably infinite alphabet (without compactification) as Borel
dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik …