Pattern sequences in ‹q, r›- numeration systems |
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Authors: | I. Shiokawa |
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Affiliation: | Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan |
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Abstract: | Let q ≥ 2 and 0 ≤ r ≤ q − 2 be integers. In this paper, we study pattern sequences for patterns in ‹q, r›-numeration systems through their generating functions. Our result implies that any nontrivial linear combination over ? of pattern sequences chosen from different ‹q, r›-numeration systems cannot be a linear recurrence sequence. In particular, pattern sequences in different ‹q, r›-numeration systems are linearly independent over ?, while within one ‹q, r›-numeration system they can be linearly dependent ?. |
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Keywords: | 11A63 11J85 |
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