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On generalised Rudin-Shapiro sequences

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Virtualconference
Authors : Stoll, Thomas (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : discrete correlation; Rudin-Shapiro sequence; difference matrix; expential sum

MSC Codes :
11A63 - Radix representation; digital problems
11K31 - Special sequences
68R15 - Combinatorics on words

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 01/12/2020
    Conference Date : 26/11/2020
    Subseries : Research talks
    arXiv category : Combinatorics ; Number Theory
    Mathematical Area(s) : Combinatorics ; Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 00:48:47
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2020-11-26_Stoll.mp4

Information on the Event

Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire
Event Organizers : Rivat, Joël ; Tichy, Robert
Dates : 23/11/2020 - 27/11/2020
Event Year : 2020
Event URL : https://www.chairejeanmorlet.com/2256.html

Citation Data

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

See Also

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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