From the Thue-Morse sequence to the apwenian sequences
Wen Wu (South China University of Technology)
Abstract: In this talk, we will introduce a class of $\pm 1$ sequences, called the apwenian sequences. The Hankel determinants of these $\pm1$ sequences share the same property as the Hankel determinants of the Thue-Morse sequence found by Allouche, Peyrière, Wen and Wen in 1998. In particular, the Hankel determinants of apwenian sequences do not vanish. This allows us to discuss the Diophantine property of the values of their generating functions at $1/b$ where $b\geq 2$ is an integer. Moreover, the number of $\pm 1$ apwenian sequences is given explicitly. Similar questions are also discussed for $0$-$1$ apwenian sequences. This talk is based on joint work with Y.-J. Guo and G.-N. Han.
dynamical systemsnumber theory
Audience: researchers in the topic
Series comments: Description: Online seminar on numeration systems and related topics
For questions or subscribing to the mailing list, contact the organisers at numeration@irif.fr
| Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
| *contact for this listing |