On multiplicatively dependent linear numeration systems, and periodic points

Conversion between Two Multiplicatively Dependent Linear Numeration Systems

Cobham's theorem for substitutions

The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then, a sequence x ∈ A...

Behavior of Digital Sequences Through Exotic Numeration Systems

Many digital functions studied in the literature, e.g., the summatory function of the base-k sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic number theory or linear algebra. In this paper we develop a method based on exotic numeration systems and we apply it on two examples motivated by the study of gen...

Pole Assignment Of Linear Discrete-Time Periodic Systems In Specified Discs Through State Feedback

The problem of pole assignment, also known as an eigenvalue assignment, in linear discrete-time periodic systems in discs was solved by a novel method which employs elementary similarity operations. The former methods tried to assign the points inside the unit circle while preserving the stability of the discrete time periodic system. Nevertheless, now we can obtain the location of eigenvalues ...

Multi-dimensional sets recognizable in all abstract numeration systems

numeration systems An abstract numeration system is a triple S = (L,Σ, <) where L is an infinite regular language over the totally ordered alphabet (Σ, <) By enumerating words of L in the radix order (induced by <), we define a one-to-one correspondence between N and L repS : N → L : n 7→ (n + 1)th word of L valS = rep −1 S : L → N Abstract numeration systems Example S = (a∗b∗, {a, b}, a < b) L...