Let be the Thue-Morse sequence, i.e., the sequence defined by the recurrence equations:
We consider , the double sequence of Hankel determinants (modulo 2) associated with the Thue-Morse sequence. Together with three other sequences, it obeys a set of sixteen recurrence equations. It is shown to be automatic. Applications are given, namely to combinatorial properties of the Thue-Morse sequence and to the existence of certain Padé approximants of the power series .
Soit la suite de Thue-Morse, c’est-à-dire la suite définie par les relations de récurrence :
Soit , la suite double des déterminants de Hankel (modulo 2) associés à la suite de Thue-Morse. Elle vérifie un ensemble complexe de relations de récurrence. On montre qu’elle est 2-automatique. On donne des applications, notamment à l’étude combinatoire de la suite de Thue-Morse et à l’existence de certains approximants de Padé de la série formelle : .
@article{AIF_1998__48_1_1_0, author = {Allouche, Jean-Paul and Peyri\`ere, Jacques and Wen, Zhi-Xiong and Wen, Zhi-Ying}, title = {Hankel determinants of the {Thue-Morse} sequence}, journal = {Annales de l'Institut Fourier}, pages = {1--27}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {1}, year = {1998}, doi = {10.5802/aif.1609}, zbl = {0974.11010}, mrnumber = {99a:11024}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1609/} }
TY - JOUR AU - Allouche, Jean-Paul AU - Peyrière, Jacques AU - Wen, Zhi-Xiong AU - Wen, Zhi-Ying TI - Hankel determinants of the Thue-Morse sequence JO - Annales de l'Institut Fourier PY - 1998 SP - 1 EP - 27 VL - 48 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1609/ DO - 10.5802/aif.1609 LA - en ID - AIF_1998__48_1_1_0 ER -
%0 Journal Article %A Allouche, Jean-Paul %A Peyrière, Jacques %A Wen, Zhi-Xiong %A Wen, Zhi-Ying %T Hankel determinants of the Thue-Morse sequence %J Annales de l'Institut Fourier %D 1998 %P 1-27 %V 48 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1609/ %R 10.5802/aif.1609 %G en %F AIF_1998__48_1_1_0
Allouche, Jean-Paul; Peyrière, Jacques; Wen, Zhi-Xiong; Wen, Zhi-Ying. Hankel determinants of the Thue-Morse sequence. Annales de l'Institut Fourier, Volume 48 (1998) no. 1, pp. 1-27. doi : 10.5802/aif.1609. https://aif.centre-mersenne.org/articles/10.5802/aif.1609/
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