arXiv
Open Access
2024
Periodicity and pure periodicity in alternate base systems
Zuzana Masáková
Edita Pelantová
Abstrak
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 system with one real base. We focus on the so-called alternate base $B$ given by a purely periodic sequence of real numbers greater than 1. We answer an open question of Charlier et al. on the set of numbers with eventually periodic $B$-expansions. We also investigate for which bases all sufficiently small rationals have a purely periodic $B$-expansion.
Topik & Kata Kunci
Penulis (2)
Z
Zuzana Masáková
E
Edita Pelantová
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2024
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