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.
Citation
Yohei Tachiya. "Algebraic independence results related to pattern sequences in distinct $\langle q,r \rangle$-numeration systems." Tohoku Math. J. (2) 64 (3) 427 - 438, 2012. https://doi.org/10.2748/tmj/1347369371
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