6 citations · 7 across the 5 of their papers we have counts for
6 papers
On biquadratic fields: when 5 squares are not enough
Daniel Dombek
In this paper we study the Pythagoras number for the rings of integers in totally real biquadratic fields . We continue the work of Tinková towards…
On distinct unit generated fields that are totally complex
Daniel Dombek, Zuzana Masáková, Volker Ziegler
We consider the problem of characterizing all number fields such that all algebraic integers can be written as the sum of distinct units of . We extend a method due…
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…
Substitutions over infinite alphabet generating (-β)-integers
Daniel Dombek
This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (-β)-expansions. We give an admissibili…
Number representation using generalized -transformation
Daniel Dombek, Zuzana Masáková, Edita Pelantová
We study non-standard number systems with negative base . Instead of the Ito-Sadahiro definition, based on the transformation of the interval $\big[-\fracβ{β+1},\frac{…
Numbers with integer expansion in the numeration system with negative base
P. Ambrož, D. Dombek, Z. Masákova +1
In this paper, we study representations of real numbers in the positional numeration system with negative basis, as introduced by Ito and Sadahiro. We focus on the set of…