Algebraic independence results related to pattern sequences in distinct $\langle q,r \rangle$-numeration systems
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- TACHIYA YOHEI
- Graduate School of Science and Technology, Hirosaki University
書誌事項
- タイトル別名
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- ALGEBRAIC INDEPENDENCE RESULTS RELATED TO PATTERN SEQUENCES IN DISTINCT $\langle\lowercase{q}, \lowercase{r}\rangle$-NUMERATION SYSTEMS
抄録
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.
収録刊行物
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- Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ
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Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ 64 (3), 427-438, 2012
東北大学大学院理学研究科数学専攻
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詳細情報 詳細情報について
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- CRID
- 1390001205119279360
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- NII論文ID
- 130005128522
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- ISSN
- 2186585X
- 00408735
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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- 使用不可