3 papers
math.DS2026
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…
math.DS2024
A dynamical view of Tijdeman's solution of the chairman assignment problem
Valérie Berthé, Olivier Carton, Nicolas Chevallier +2
In 1980, R. Tijdeman provided an on-line algorithm that generates sequences over a finite alphabet with minimal discrepancy, that is, such that the occurrence of each letter optima…
math.NT2024
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…