7 citations · 16 across the 8 of their papers we have counts for
10 papers
Periodic representations in Salem bases
Tomáš Vávra
We prove that all algebraic bases allow an eventually periodic representations of the elements of with a finite alphabet of digits . Moreover, the cl…
Periodic representations in algebraic bases
Vítězslav Kala, Tomáš Vávra
We study periodic representations in number systems with an algebraic base (not a rational integer). We show that if has no Galois conjugate on the unit circle, then there…
Finite beta-expansions with negative bases
Zuzana Krčmáriková, Wolfgang Steiner, Tomáš Vávra
The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers having the negative finiteness property, that is the set o…
On the spectra of Pisot-cyclotomic numbers
Kevin G. Hare, Zuzana Masáková, Tomáš Vávra
We investigate the complex spectra \[ X^{\mathcal A}(β)=\left\{\sum_{j=0}^na_jβ^j : n\in{\mathbb N},\ a_j\in{\mathcal A}\right\} \] where is a quadratic or cubic Pisot-cyclotom…
Pisot unit generators in number fields
Tomáš Vávra, Francesco Veneziano
Pisot numbers are real algebraic integers bigger than 1, whose other conjugates have all modulus smaller than 1. In this paper we deal with the algorithmic problem of finding the s…
On the Finiteness property of negative cubic Pisot bases
Tomáš Vávra
We study arithmetical aspects of Ito-Sadahiro number systems with negative base. We show that the bases , where is zero of possess the s…
Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems
Daniel Dombek, Zuzana Masáková, Tomáš Vávra
In this paper we study the expansions of real numbers in positive and negative real base as introduced by Rényi, and Ito & Sadahiro, respectively. In particular, we compare the set…
Integers in number systems with positive and negative quadratic Pisot base
Zuzana Masáková, Tomáš Vávra
We consider numeration systems with base and , for quadratic Pisot numbers and focus on comparing the combinatorial structure of the sets and of number…
Arithmetics in numeration systems with negative quadratic base
Z. Masáková, T. Vávra
We consider positional numeration system with negative base , as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when is…
Arithmetics in number systems with negative base
Z. Masáková, E. Pelantová, T. Vávra
We study the numeration system with negative basis, introduced by Ito and Sadahiro. We focus on arithmetic operations in the set and of numbers having fin…