On the boundary sequence of an automatic sequence |
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| Affiliation: | 1. Institute of Applied Mathematics, College of Science, Huazhong Agricultural University, 430070, Wuhan, PR China;2. School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074, Wuhan, PR China |
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| Abstract: | In this paper, we prove a conjecture of Chen and Wen that the boundary sequence of an automatic sequence is also automatic. In particular, we study the boundary sequences of the generalized Cantor sequences, and give a complete characterization of the periodic boundary sequences. As an application, for a class of automatic sequences, we prove that their abelian complexities are also automatic. |
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| Keywords: | Generalized Cantor sequence Automatic sequence Boundary sequence Abelian complexity |
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