ALGEBRAIC INDEPENDENCE RESULTS RELATED TO PATTERN SEQUENCES IN DISTINCT $\langle\lowercase{q}, \lowercase{r}\rangle$-NUMERATION SYSTEMS
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- TACHIYA YOHEI
- Graduate School of Science and Technology, Hirosaki University
Bibliographic Information
- Other Title
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- Algebraic independence results related to pattern sequences in distinct $\langle q,r \rangle$-numeration systems
Abstract
In this paper, we prove the algebraic independence over $\boldsymbol{C}(z)$ of the generating functions of pattern sequences defined in distinct $\langle q, r\rangle$-numeration systems. Our result asserts that any nontrivial linear combination over $\boldsymbol{C}$ of pattern sequences chosen from distinct $\langle q, r \rangle$-numeration systems can not be a linear recurrence sequence. As an application, we give a linear independence over $\boldsymbol{C}$ of the pattern sequences.
Journal
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- Tohoku Mathematical Journal, Second Series
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Tohoku Mathematical Journal, Second Series 64 (3), 427-438, 2012
Mathematical Institute, Tohoku University
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Keywords
Details 詳細情報について
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- CRID
- 1390001205119279360
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- NII Article ID
- 130005128522
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- ISSN
- 2186585X
- 00408735
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed