Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

14 28

On generalised Rudin-Shapiro sequences

By Thomas Stoll

We introduce a family of block-additive automatic sequences, that are obtained by allocating a weight to each couple of digits, and defining the nth term of the sequence as being the total weight of the integer n written in base k. Under an additional combinatorial difference condition on the weight function, these sequences can be interpreted as generalised Rudin–Shapiro sequences. We prove that these sequences have the same two-term correlations as sequences of symbols chosen uniformly and independently at random. The speed of convergence is independent of the prime factor decomposition of k. This extends work by E. Grant, J. Shallit, T. Stoll, and by P.-A. Tahay.

Information about the video

Date of recording 26/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19689403
Cite this video Stoll, Thomas (26/11/2020). On generalised Rudin-Shapiro sequences. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19689403
URL https://dx.doi.org/10.24350/CIRM.V.19689403

Domain(s)

Bibliography

GRANT, E., SHALLIT, J., et STOLL, T. Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences. Acta Arithmetica, 2009, vol. 140, no 4, p. 345-368. - http://dx.doi.org/10.4064/aa140-4-5
Tahay, P. (2020). Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size, Uniform distribution theory, 15(1), 1-26 - https://doi.org/10.2478/udt-2020-0001
MARCOVICI, Irène, STOLL, Thomas, et TAHAY, Pierre-Adrien. Discrete correlations of order 2 of generalised Rudin-Shapiro sequences: a combinatorial approach. arXiv preprint arXiv:2006.13162, 2020. - https://arxiv.org/abs/2006.13162

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