5 papers
2-balanced sequences coding rectangle exchange transformation
Lubomíra Dvořáková, Zuzana Masáková, Edita Pelantová
We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any gi…
Periodicity and pure periodicity in alternate base systems
Zuzana Masáková, Edita Pelantová
We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence of integer bases and the Rényi…
Midy's Theorem in non-integer bases and divisibility of Fibonacci numbers
Zuzana Masáková, Edita Pelantová
Fractions with prime denominator written in decimal have a curious property described by Midy's Theorem, namely that two halves of their period (if it i…
On periodic representations in non-Pisot bases
Simon Baker, Zuzana Masáková, Edita Pelantová +1
We study periodic expansions in positional number systems with a base $β\in\C,\ |β|>1$, and with coefficients in a finite set of digits $\A\subset\C.$ We are interested in determin…
Palindromic complexity of infinite words associated with simple Parry numbers
Petr Ambrož, Christiane Frougny, Zuzana Masáková +1
A simple Parry number is a real number β>1 such that the Rényi expansion of 1 is finite, of the form d_β(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic word…