BETA CANTOR SERIES EXPANSION AND ADMISSIBLE SEQUENCES
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| Název: | BETA CANTOR SERIES EXPANSION AND ADMISSIBLE SEQUENCES |
|---|---|
| Autoři: | Jonathan Caalim, Shiela Demegillo |
| Zdroj: | Acta Polytechnica, Vol 60, Iss 3, Pp 214-224 (2020) |
| Informace o vydavateli: | Czech Technical University in Prague - Central Library, 2020. |
| Rok vydání: | 2020 |
| Témata: | beta expansion, q-cantor series expansion, numeration system, admissibility, Automata Theory and Formal Languages, 01 natural sciences, Computational Complexity and Algorithmic Information Theory, FOS: Mathematics, Series (stratigraphy), Genetics, Alphabet, 0101 mathematics, Biology, Mathematical Physics, BETA (programming language), Regular Expressions, Paleontology, Linguistics, Discrete mathematics, Engineering (General). Civil engineering (General), Computer science, FOS: Philosophy, ethics and religion, Programming language, Philosophy, Computational Theory and Mathematics, Combinatorics, FOS: Biological sciences, Computer Science, Physical Sciences, Dynamical Systems and Chaos Theory, FOS: Languages and literature, Integer (computer science), TA1-2040, Mathematics, Sequence (biology) |
| Popis: | We introduce a numeration system, called the beta Cantor series expansion, that generalizes the classical positive and negative beta expansions by allowing non-integer bases in the Q-Cantor series expansion. In particular, we show that for a fix $\gamma \in \mathbb{R}$ and a sequence $B=\{\beta_i\}$ of real number bases, every element of the interval $x \in [\gamma,\gamma+1)$ has a beta Cantor series expansion with respect to B where the digits are integers in some alphabet $\mathcal{A}(B)$. We give a criterion in determining whether an integer sequence is admissible when $B$ satisfies some condition. We provide a description of the reference strings, namely the expansion of $\gamma$ and $\gamma+1$, used in the admissibility criterion. |
| Druh dokumentu: | Article Other literature type |
| ISSN: | 1805-2363 1210-2709 |
| DOI: | 10.14311/ap.2020.60.0214 |
| DOI: | 10.60692/2k4ek-6we35 |
| DOI: | 10.60692/cpmwc-s3r87 |
| Přístupová URL adresa: | https://ojs.cvut.cz/ojs/index.php/ap/article/download/5897/5778 https://doaj.org/article/c56fa8a0b4c3432eb834b0f79037f3ab |
| Rights: | CC BY |
| Přístupové číslo: | edsair.doi.dedup.....f0e9f22e0961c5f07ee1f78ac723335c |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We introduce a numeration system, called the beta Cantor series expansion, that generalizes the classical positive and negative beta expansions by allowing non-integer bases in the Q-Cantor series expansion. In particular, we show that for a fix $\gamma \in \mathbb{R}$ and a sequence $B=\{\beta_i\}$ of real number bases, every element of the interval $x \in [\gamma,\gamma+1)$ has a beta Cantor series expansion with respect to B where the digits are integers in some alphabet $\mathcal{A}(B)$. We give a criterion in determining whether an integer sequence is admissible when $B$ satisfies some condition. We provide a description of the reference strings, namely the expansion of $\gamma$ and $\gamma+1$, used in the admissibility criterion. |
|---|---|
| ISSN: | 18052363 12102709 |
| DOI: | 10.14311/ap.2020.60.0214 |