10 papers
From some Pisot numerations to topological groups
Olivier Carton, Jake Sudbery, Reem Yassawi
A Pisot numeration system for is a sequence of natural numbers generated by an integral homogeneous linear recurrence whose characteristic polynomial is the minimal…
Algebraic power series and their automatic complexity modulo prime powers
Eric Rowland, Reem Yassawi
Christol and, independently, Denef and Lipshitz showed that an algebraic sequence of -adic integers (or integers) is -automatic when reduced modulo . Previously, the be…
When is the Ellis semigroup a complete conjugacy invariant?
Johannes Kellendonk, Reem Yassawi
The Ellis semigroup of a topological dynamical system contains algebraic, topological and dynamical information. It is invariant under conjugacy. Despite this wealth of structure,…
Mahler equations for Zeckendorf numeration
Olivier Carton, Reem Yassawi
We define generalised equations of Z-Mahler type, based on the Zeckendorf numeration system. We show that if a sequence over a commutative ring is Z-regular, then it is the sequenc…
Cobham's theorem for the Gaussian integers
Ãlvaro Bustos-Gajardo, Álvaro Bustos-Gajardo, Robbert Fokkink +1
Assuming the four exponentials conjecture, Hansel and Safer showed that if a subset of the Gaussian integers is both - and -recognizable, then it is syndetic,…
Meyer sets, Pisot numbers, and self-similarity in symbolic dynamical systems
Valérie Berthé, Reem Yassawi
Aperiodic order refers to the mathematical formalisation of quasicrystals. Substitutions and cut and project sets are among their main actors; they also play a key role in the stud…